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Emeritus Professor Mirka Miller

Conjoint Professor

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Mirka Miller was awarded PhD from The University of New South Wales in 1990. Since then she has held senior academic positions at the University of New England, and The University of Newcastle, where she was Assistant Dean (Research Postgraduates) and, for a time, the only female academic member of the Faculty of Engineering. Between 2004 and 2008 she was Professor of Computer Science at the University of Ballarat. Since April 2008 she is Professor in the School of Electrical Engineering and Computer Science, The University of Newcastle, and the Leader of the GTA research group. Additionally, since 2001 Professor Miller has been Conjoint Professor at the University of West Bohemia, Pilsen, Czech Republic.

Research Expertise

Professor Miller's principal areas of research are broadly classified as Graph Theory and Data Security. In Graph Theory she has made considerable advances in the fields of Graph Labellings, Graph Algorithms and Graph Applications. Her work on Extremal Graph Theory has won her international renown. In this difficult and complex area working on fundamental properties of graphs she has published many deep results, even giving her name to a class of graphs, the McKay, Miller, Siran Graphs. With Prof Jozef Siran she is author of the much cited Moore Bound and Beyond: A Dynamic Survey of the Degree, Diameter Problem. She is currently writing a book on Graph Labelling. Professor Miller's other area of research is Data Security, especially in the Security of Statistical Databases. 


Qualifications

  • PhD, University of New South Wales
  • Master of Arts, University of New England
  • Bachelor of Arts, University of Sydney
  • Master of Letters, University of New England

Keywords

  • combinatorics
  • data security
  • graph theory

Languages

  • Czech (Fluent)

Fields of Research

Code Description Percentage
010199 Pure Mathematics not elsewhere classified 40
080299 Computation Theory and Mathematics not elsewhere classified 55
019999 Mathematical Sciences not elsewhere classified 5

Professional Experience

UON Appointment

Title Organisation / Department

Academic appointment

Dates Title Organisation / Department
1/03/2004 - 1/03/2008 Professor of Computer Science University of Ballarat
School of ITMS- Computer Science
Australia
1/01/1999 - 1/02/2004 Associate Professor University of Newcastle
School of Elect Engineering and Computer Science
Australia
1/01/1992 - 1/12/1998 Senior Lecturer University of Newcastle
Academic Division- Computer Science
Australia
1/01/1983 - 1/12/1991 Lecturer University of New England
Department of Mathematics, Statistics and Computer Science
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (2 outputs)

Year Citation Altmetrics Link
2008 Baca M, Miller M, Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions, Brown Walker Press, Boca Raton, Florida, 227 (2008) [A1]
2005 Ryan J, Manyem P, Miller M, Sugeng KA, Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms, University of Ballarat - School of Information Technology & Mathematical Sciences, Ballarat, Victoria, Australia, 400 (2005) [A3]

Chapter (1 outputs)

Year Citation Altmetrics Link
2013 Kratochvil J, Miller M, 'Preface', , ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD 1-2 (2013) [C3]
DOI 10.1016/j.ejc.2012.07.009

Journal article (180 outputs)

Year Citation Altmetrics Link
2015 Abawajy J, Kelarev AV, Miller M, Ryan J, 'Rees semigroups of digraphs for classification of data', Semigroup Forum, (2015)

Recent research has motivated the investigation of the weights of ideals in semiring constructions based on semigroups. The present paper introduces Rees semigroups of directed gr... [more]

Recent research has motivated the investigation of the weights of ideals in semiring constructions based on semigroups. The present paper introduces Rees semigroups of directed graphs. This new construction is a common generalization of Rees matrix semigroups and incidence semigroups of digraphs. For each finite subsemigroup (Formula presented.) of the Rees semigroup of a digraph and for every zero-divisor-free idempotent semiring (Formula presented.) with identity element, our main theorem describes all ideals (Formula presented.) in the semigroup semiring (Formula presented.) such that (Formula presented.) has the largest possible weight.

DOI 10.1007/s00233-014-9685-x
2015 Gómez J, Miller M, 'On the existence of radial Moore graphs for every radius and every degree', European Journal of Combinatorics, 47 15-22 (2015)

The degree/diameter problem is to determine the largest graphs of given maximum degree and given diameter. General upper bounds-called Moore bounds-for the order of such graphs ar... [more]

The degree/diameter problem is to determine the largest graphs of given maximum degree and given diameter. General upper bounds-called Moore bounds-for the order of such graphs are attainable only for certain special graphs, called Moore graphs. Moore graphs are scarce and so the next challenge is to find graphs which are somehow "close" to the nonexistent ideal of a Moore graph by holding fixed two of the parameters, order, diameter and maximum degree, and optimising the third parameter. In this paper we consider the existence of graphs that have order equal to Moore bound for given radius and maximum degree and as the relaxation we require the diameter to be at most one more than the radius. Such graphs are called radial Moore graphs. In this paper we prove that radial Moore graphs exist for every diameter and every sufficiently large degree, depending on the diameter.

DOI 10.1016/j.ejc.2015.01.004
2015 Baca M, Miller M, Phanalasy O, Ryan J, Semanicová-Fenovcíková A, Sillasen AA, 'Totally antimagic total graphs', Australasian Journal of Combinatorics, 61 42-56 (2015)

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . ., |V(G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the su... [more]

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . ., |V(G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-antimagic total (vertexantimagic total) if all edge-weights (vertex-weights) are pairwise distinct. If a labeling is simultaneously edge-antimagic total and vertex-antimagic total it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph.

2015 Daykin JW, Iliopoulos CS, Miller M, Phanalasy O, 'Antimagicness of Generalized Corona and Snowflake Graphs', Mathematics in Computer Science, 9 105-111 (2015)
DOI 10.1007/s11786-014-0213-x
2015 Stephen S, Rajan B, Miller M, Grigorious C, William A, 'On the energy of certain recursive structures', Journal of Combinatorial Mathematics and Combinatorial Computing, 92 215-222 (2015)
2015 Conde J, Miller M, Miret JM, Saurav K, 'On the Nonexistence of Almost Moore Digraphs of Degree Four and Five', Mathematics in Computer Science, 9 145-149 (2015)
DOI 10.1007/s11786-015-0219-z
2015 Abawajy J, Kelarev AV, Miller M, Ryan J, 'Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications', Mathematics in Computer Science, 9 127-137 (2015)

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest ... [more]

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

DOI 10.1007/s11786-015-0217-1
2015 Miller M, Rajan B, Rajasingh I, 'Foreword', Mathematics in Computer Science, 9 125-126 (2015)
DOI 10.1007/s11786-015-0235-z
2015 RIZVI STR, KHALID M, ALI K, MILLER M, RYAN J, 'ON CYCLE-SUPERMAGICNESS OF SUBDIVIDED GRAPHS', Bulletin of the Australian Mathematical Society, (2015)

Lladó and Moragas [¿Cycle-magic graphs¿, Discrete Math. 307 (2007), 2925¿2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. ... [more]

Lladó and Moragas [¿Cycle-magic graphs¿, Discrete Math. 307 (2007), 2925¿2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. They discussed cycle-magic labellings of subdivided wheels and friendship graphs, but there are no further results on cycle-magic labellings of other families of subdivided graphs. In this paper, we find cycle-magic labellings for subdivided graphs. We show that if a graph has a cycle-(super)magic labelling, then its uniform subdivided graph also has a cycle-(super)magic labelling. We also discuss some cycle-supermagic labellings for nonuniform subdivided fans and triangular ladders.

DOI 10.1017/S0004972715000325
2015 Conde J, Miller M, Miret JM, Saurav K, 'On the Nonexistence of Almost Moore Digraphs of Degree Four and Five', Mathematics in Computer Science, (2015)

An almost Moore (d, k)-digraph is a regular digraph of degree (Formula presented.), diameter (Formula presented.) and order (Formula presented.). So far, their existence has only ... [more]

An almost Moore (d, k)-digraph is a regular digraph of degree (Formula presented.), diameter (Formula presented.) and order (Formula presented.). So far, their existence has only been showed for k = 2. Their nonexistence has been proved for k = 3, 4 and for d = 2, 3 when (Formula presented.). In this paper, we prove that (4, k) and (5, k)-digraphs with self-repeats do not exist for infinitely many primes k.

DOI 10.1007/s11786-015-0219-z
2015 Abawajy J, Kelarev AV, Miller M, Ryan J, 'Distances of Centroid Sets in a Graph-Based Construction for Information Security Applications', Mathematics in Computer Science, (2015)

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest ... [more]

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

DOI 10.1007/s11786-015-0217-1
2015 Miller M, Rajan B, Rajasingh I, 'Foreword', Mathematics in Computer Science, (2015)
DOI 10.1007/s11786-015-0235-z
2014 Abawajy J, Kelarev AV, Miller M, Ryan J, 'Incidence semirings of graphs and visible bases', Bulletin of the Australian Mathematical Society, 89 451-459 (2014) [C1]
DOI 10.1017/S000497271300083X
2014 Grigorious C, Stephen S, Rajan B, Miller M, William A, 'On the partition dimension of a class of circulant graphs', INFORMATION PROCESSING LETTERS, 114 353-356 (2014) [C1]
DOI 10.1016/j.ipl.2014.02.005
Citations Scopus - 1
2014 Grigorious C, Manuel P, Miller M, Rajan B, Stephen S, 'On the metric dimension of circulant and Harary graphs', Applied Mathematics and Computation, 248 47-54 (2014) [C1]

A metric generator is a set W of vertices of a graph G(V,E) such that for every pair of vertices u,v of G, there exists a vertex w¿W with the condition that the length of a short... [more]

A metric generator is a set W of vertices of a graph G(V,E) such that for every pair of vertices u,v of G, there exists a vertex w¿W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. In this case the vertex w is said to resolve or distinguish the vertices u and v. The minimum cardinality of a metric generator for G is called the metric dimension. The metric dimension problem is to find a minimum metric generator in a graph G. In this paper, we make a significant advance on the metric dimension problem for circulant graphs C(n,±{1,2,...,j}),1=j= ¿n/2¿,n=3, and for Harary graphs.

DOI 10.1016/j.amc.2014.09.045
Citations Scopus - 1
2014 Holub P, Miller M, Perez-Roses H, Ryan J, 'Degree diameter problem on honeycomb networks', DISCRETE APPLIED MATHEMATICS, 179 139-151 (2014) [C1]
DOI 10.1016/j.dam.2014.07.012
2014 Holub P, Miller M, Pérez-Rosés H, Ryan J, 'Degree diameter problem on honeycomb networks', Discrete Applied Mathematics, (2014) [C1]

The degree diameter problem involves finding the largest graph (in terms of the number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the ... [more]

The degree diameter problem involves finding the largest graph (in terms of the number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalization of this problem, the graph is considered to be embedded in some connected host graph, in this paper the honeycomb network. We consider embedding the graph in the k-dimensional honeycomb grid and provide upper and lower bounds for the optimal graph. The particular cases of dimensions 2 and 3 are examined in detail. © 2014 Elsevier B.V. All rights reserved.

DOI 10.1016/j.dam.2014.07.012
2014 Conde J, Gimbert J, Gonzalez J, Miller M, Miret JM, 'On the nonexistence of almost Moore digraphs', EUROPEAN JOURNAL OF COMBINATORICS, 39 170-177 (2014) [C1]
DOI 10.1016/j.ejc.2013.12.003
2014 Christou M, Iliopoulos CS, Miller M, 'Maximizing the size of planar graphs under girth constraints', Journal of Combinatorial Mathematics and Combinatorial Computing, 89 129-141 (2014) [C1]

In 1975, Erdos proposed the problem of determining the maximal number of edges in a graph on n vertices that contains no triangles or squares. In this paper we consider a generali... [more]

In 1975, Erdos proposed the problem of determining the maximal number of edges in a graph on n vertices that contains no triangles or squares. In this paper we consider a generalized version of the problem, i.e. what is the maximum size, ex(n;t), of a graph of order n and girth at least t + 1 (containing no cycles of length less than t +1). The set of those extremal Ct-free graphs is denoted by EX(n;t). We consider the problem on special types of graphs, such as pseudotrees, cacti, graphs lying in a square grid, Halin, generalized Halin and planar graphs. We give the extremal cases, some constructions and we use these results to obtain general lower bounds for the problem in the general case.

2014 Arumugam S, Miller M, Phanalasy O, Ryan J, 'Antimagic labeling of generalized pyramid graphs', ACTA MATHEMATICA SINICA-ENGLISH SERIES, 30 283-290 (2014) [C1]
DOI 10.1007/s10114-014-2381-7
Citations Scopus - 1
2014 ABAWAJY J, KELAREV AV, MILLER M, RYAN J, 'Incidence Semirings of Graphs and Visible Bases', Bulletin of the Australian Mathematical Society, 89 451-459 (2014) [C1]
DOI 10.1017/S000497271300083X
2014 Buset D, Miller M, Phanalasy O, Ryan J, 'Antimagicness for a family of generalized antiprism graphs', Electronic Journal of Graph Theory and Applications, 2 42-51 (2014) [C1]
DOI 10.5614/ejgta.2014.2.1.4
2014 Brankovic L, Lopez N, Miller M, Sebe F, 'Triangle randomization for social network data anonymization', Ars Mathematica Contemporanea, 7 461-477 (2014) [C1]
Co-authors Ljiljana Brankovic
2013 Miller M, Sundara Rajan R, Parthiban N, Rajasingh I, 'Minimum linear arrangement of incomplete hypercubes', Computer Journal, 58 331-337 (2013)
DOI 10.1093/comjnl/bxu031
2013 Feria-Puron R, Miller M, Pineda-Villavicencio G, 'On large bipartite graphs of diameter 3', DISCRETE MATHEMATICS, 313 381-390 (2013) [C1]
DOI 10.1016/j.disc.2012.11.013
2013 Balbuena C, Miller M, ¿irán J, ¿dímalová M, 'Large vertex-transitive graphs of diameter 2 from incidence graphs of biaffine planes', Discrete Mathematics, 313 2014-2019 (2013) [C1]
DOI 10.1016/j.disc.2013.03.007
2013 Miller M, Ryan J, Ryjacek Z, Teska J, Vrana P, 'Stability of hereditary graph classes under closure operations', Journal of Graph Theory, 74 67-80 (2013) [C1]
DOI 10.1002/jgt.21692
2013 Marzuki CC, Salman ANM, Miller M, 'On the total irregularity strength of cycles and paths', Far East Journal of Mathematical Sciences, 82 1-21 (2013) [C1]

The vertex irregular total labeling and the edge irregular total labeling were introduced by Baca et al. in [5]. Combining both of these notions, in this paper, we introduce a new... [more]

The vertex irregular total labeling and the edge irregular total labeling were introduced by Baca et al. in [5]. Combining both of these notions, in this paper, we introduce a new irregular total labeling, called 'totally irregular total labeling' which is required to be both vertex and edge irregular. Let G = (V, E) be a graph. A function f : V¿E ¿ {1, 2, ..., k} of a graph G is a totally irregular total k-labeling if for any two different vertices x and y of G, their weights wt(x) and wt(y) are distinct and for any two different edges x1x2 and y1y2 of G, their weights wt(x1x2) and wt(y1y2) are distinct, where the weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x, and the weight wt(x1x2) of an edge x1x2 is the sum of the label of edge x1x2 and the labels of vertices x1 and x2. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we provide an upper bound and a lower bound of the total irregularity strength of a graph. Besides that, we determine the total irregularity strength of cycles and paths. © 2013 Pushpa Publishing House, Allahabad, India.

Citations Scopus - 1
2013 Christou M, Iliopoulos CS, Miller M, 'Degree/diameter problem for trees and pseudotrees', AKCE International Journal of Graphs and Combinatorics, 10 377-389 (2013) [C2]

The degree/diameter problem asks: Given natural numbers d and k what is the order (that is, the maximum number of vertices) nd,k that can be contained in a graph of maximum degree... [more]

The degree/diameter problem asks: Given natural numbers d and k what is the order (that is, the maximum number of vertices) nd,k that can be contained in a graph of maximum degree d and diameter at most k? The degree/diameter problem is wide open for most values of d and k. A general upper bound exists; it is called the Moore bound. Graphs whose order attains the Moore bound are called Moore graphs. Since the degree/diameter problem is considered to be very difficult in general, it is worthwhile to consider it for special classes of graphs. In this paper we consider the degree/diameter problem on trees, special types of trees such as Cayley trees, caterpillars, lobsters, banana trees and firecracker trees, as well as for tree-like structures such as pseudotrees. We obtain new nd,k values and provide corresponding constructions.

2013 Miller M, Phanalasy O, Ryan J, Rylands L, 'Sparse graphs with vertex antimagic edge labelings', AKCE International Journal of Graphs and Combinatorics, 10 193-198 (2013) [C1]
Citations Scopus - 1
2013 Rahmawati S, Sugeng KA, Silaban DR, Miller M, Baca M, 'Construction of new larger (a, d)-edge antimagic vertex graphs by using adjacency matrices', Australasian Journal of Combinatorics, 56 257-272 (2013) [C1]
2013 Miller M, Ryan J, Ryjácek Z, 'Distance-locally disconnected graphs', Discussiones Mathematicae - Graph Theory, 33 203-215 (2013) [C1]

For an integer k = 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ¿ V (G), the set of vert... [more]

For an integer k = 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ¿ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is I(n2) for any fixed value of k and, in the special case of regular graphs, we show that this asymptotic rate of growth cannot be achieved. For regular graphs, we give a general upper bound and we show its asymptotic sharpness for some values of k. We also discuss some connections with cages.

DOI 10.7151/dmgt.1657
2013 Ali K, Hussain M, Ahmad A, Miller M, 'Magic Labelings of Type (a, b, c) of Families of Wheels', Mathematics in Computer Science, 7 315-319 (2013) [C1]
DOI 10.1007/s11786-013-0162-9
2012 Miller M, Pérez-Rosés H, Ryan J, 'The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh', CoRR, abs/1203.4069 (2012)
2012 Iliopoulos CS, Miller M, Pissis SP, 'Parallel algorithms for mapping short degenerate and weighted DNA sequences to a reference genome', International Journal of Foundations of Computer Science, 23 249-259 (2012) [C1]
2012 Miller M, Perez-Roses H, Ryan JF, 'The maximum degree and diameter-bounded subgraph in the mesh', Discrete Applied Mathematics, 160 1782-1790 (2012) [C1]
Citations Scopus - 1Web of Science - 1
2012 Miller M, Phanalasy O, Ryan JF, Rylands L, 'Antimagicness of some families of generalized graphs', Australasian Journal of Combinatorics, 53 179-190 (2012) [C1]
2011 Marshall KL, Miller M, Ryan JF, 'Extremal graphs without cycles of length 8 or less', Electronic Notes in Discrete Mathematics, 38 615-620 (2011) [C2]
DOI 10.1016/j.endm.2011.10.003
2011 Miller M, Phanalasy O, Ryan JF, 'All graphs have antimagic total labelings', Electronic Notes in Discrete Mathematics, 38 645-650 (2011) [C1]
Citations Scopus - 1
2011 Phanalasy O, Miller M, Iliopoulos CS, Pissis SP, Vaezpour E, 'Construction of antimagic labeling for the Cartesian product of regular graphs', Mathematics in Computer Science, 5 81-87 (2011) [C1]
2011 Miller M, Rajan B, Ryan JF, 'Foreword', Mathematics in Computer Science, 5 1-2 (2011) [C3]
2011 Feria Puron R, Miller M, Pineda-Villavicencio G, 'On graphs of defect at most 2', Discrete Applied Mathematics, 159 1331-1344 (2011) [C1]
DOI 10.1016/j.dam.2011.04.018
Citations Scopus - 3Web of Science - 3
2011 Loz E, Macaj M, Miller M, Siagiova J, Siran J, Tomanova J, 'Small vertex-transitive and Cayley graphs of girth six and given degree: An algebraic approach', Journal of Graph Theory, 68 265-284 (2011) [C1]
DOI 10.1002/jgt.20556
Citations Scopus - 2Web of Science - 1
2011 Dafik, Miller M, Ryan J, Baca M, 'Super edge-antimagic total labelings of mK,n,n', ARS COMBINATORIA, 101 97-107 (2011) [C1]
Citations Scopus - 2Web of Science - 1
2011 Rylands L, Phanalasy O, Ryan JF, Miller M, 'Construction for antimagic generalized web graphs', AKCE International Journal of Graphs and Combinatorics, 8 141-149 (2011) [C1]
Citations Scopus - 1
2011 Sugeng KA, Herawati BN, Miller M, Baca M, 'On magicness and antimagicness of the union of 4-regular circulant graphs', Australasian Journal of Combinatorics, 50 141-153 (2011) [C1]
2011 Miller M, 'Nonexistence of graphs with cyclic defect', Electronic Journal of Combinatorics, 18 1-5 (2011) [C1]
2010 Tang J, Lin Y, Miller M, 'New results on EX graphs', Mathematics in Computer Science, 3 119-126 (2010) [C1]
DOI 10.1007/s11786-009-0009-6
Citations Scopus - 1
Co-authors Yuqing Lin
2010 Miller M, Wada K, 'Foreword', Mathematics in Computer Science, 3 1-2 (2010) [C3]
2010 Maryati TK, Salman ANM, Baskoro ET, Ryan JF, Miller M, 'On H-supermagic labelings for certain shackles and amalgamations of a connected graph', Utilitas Mathematica, 83 333-342 (2010) [C1]
Citations Scopus - 6Web of Science - 4
2010 Nguyen HM, Miller M, 'Structural properties of graphs of diameter 2 and defect 2', AKCE Journal of Graphs and Combinatronics, 7 29-43 (2010) [C1]
2010 Baca M, Miller M, Phanalasy O, Semanicova-Fenovcikova A, 'Super d-antimagic labelings of disconnected plane graphs', Acta Mathematica Sinica, English Series, 26 2283-2294 (2010) [C1]
DOI 10.1007/s10114-010-9502-8
Citations Scopus - 7Web of Science - 4
2009 Delorme C, Flandrin E, Lin Y, Miller M, Ryan JF, 'On extremal graphs with bounded girth', Electronic Notes in Discrete Mathematics, 34 653-657 (2009) [C2]
DOI 10.1016/j.endm.2009.07.110
Citations Scopus - 1
Co-authors Yuqing Lin
2009 Miller M, ¿irán J, 'Moore graphs and beyond: A survey of the degree/diameter problem', Electronic Journal of Combinatorics, 1-61 (2009) [C1]

The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds - called Moore bounds - for the order o... [more]

The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds - called Moore bounds - for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bounds for the maxi- mum possible number of vertices, given the other two parameters, and thus attack- ing the degree/diameter problem 'from above', remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter problem 'from below'. This survey aims to give an overview of the current state-of-the-art of the degree/diameter problem. We focus mainly on the above two streams of research. However, we could not resist mentioning also results on various related problems. These include considering Moore-like bounds for special types of graphs and digraphs, such as vertex-transitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.

Citations Scopus - 30
2009 Dafik, Miller M, Ryan JF, Baca M, 'On super (a, d)-edge-antimagic total labeling of disconnected graphs', Discrete Mathematics, 309 4909-4915 (2009) [C1]
DOI 10.1016/j.disc.2008.04.031
Citations Scopus - 7Web of Science - 1
2009 Pineda-Villavicencio G, Gomez J, Miller M, Perez-Roses H, 'New largest known graphs of diameter 6', Networks, 53 315-328 (2009) [C1]
DOI 10.1002/net.20269
Citations Scopus - 2Web of Science - 2
2009 Miller M, Pineda-Villavicencio G, 'Complete catalogue of graphs of maximum degree 3 and defect at most 4', Discrete Applied Mathematics, 157 2983-2996 (2009) [C1]
DOI 10.1016/j.dam.2009.04.021
Citations Scopus - 3Web of Science - 3
2009 Lin Y, Balbuena C, Miller M, 'On the number of components of (k, g)-cages after vertex deletion', Discrete Applied Mathematics, 157 1760-1765 (2009) [C1]
DOI 10.1016/j.dam.2008.12.005
Co-authors Yuqing Lin
2009 Tang J, Lin Y, Balbuena C, Miller M, 'Calculating the extremal number ex (v ; {C3, C4, ..., Cn})', Discrete Applied Mathematics, 157 2198-2206 (2009) [C1]
DOI 10.1016/j.dam.2007.10.029
Citations Scopus - 8Web of Science - 5
Co-authors Yuqing Lin
2009 Tang J, Lin Y, Balbuena C, Miller M, 'Calculating the extremal number ex (v ; {C3, C4, ..., Cn})', Discrete Applied Mathematics, 157 2198-2206 (2009) [C1]
DOI 10.1016/j.dam.2007.10.029
Co-authors Yuqing Lin
2009 Delorme C, Jorgensen LK, Miller M, Pineda-Villavicencio G, 'On bipartite graphs of defect 2', European Journal of Combinatorics, 30 798-808 (2009) [C1]
DOI 10.1016/j.ejc.2008.09.030
Citations Scopus - 4Web of Science - 4
2009 Baca M, Dafik, Miller M, Ryan J, 'Antimagic labeling of disjoint union of s-crowns', Utilitas Mathematica, 79 193-205 (2009) [C1]
Citations Scopus - 3Web of Science - 2
2009 Delorme C, Jorgensen LK, Miller M, Pineda-Villavicencio G, 'On bipartite graphs of diameter 3 and defect 2', Journal of Graph Theory, 61 271-288 (2009) [C1]
DOI 10.1002/jgt.20378
Citations Scopus - 4Web of Science - 3
2009 Dafik, Miller M, Iliopoulos C, Ryjacek Z, 'On diregularity of digraphs of defect at most two', Journal of Combinatorial Mathematics and Combinatorial Computing, 71 21-37 (2009) [C1]
2009 Miller M, Nguyen MH, Pineda-Villavicencio G, 'On the nonexistence of graphs of diameter 2 and defect 2', Journal of Combinatorial Mathematics and Combinatorial Computing, 71 5-20 (2009) [C1]
Citations Scopus - 2
2009 Sugeng KA, Froncek D, Miller M, Ryan JF, Walker J, 'On distance magic labeling of graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 71 39-48 (2009) [C1]
Citations Scopus - 7
2009 Arumugam S, Bloom GS, Miller M, Ryan JF, 'Some open problems on graph labelings', AKCE International Journal of Graphs and Combinatorics, 6 229-236 (2009) [C1]
2009 Arumugam S, Bloom GS, Bu C, Miller M, Rao SB, Ryan JF, 'Guest editors', AKCE International Journal of Graphs and Combinatorics, 6 (2009) [C2]
2009 Gimbert J, Lopez N, Miller M, Ryan JF, 'On the period and tail of sequences of iterated eccentric digraphs', Bulletin of the Institute of Combinatorics and its Applications, 56 19-32 (2009) [C1]
2008 Dafik, Miller M, Ryan JF, Baca M, 'Antimagic labeling of the union of two stars', The Australasian Journal of Combinatorics, 42 35-44 (2008) [C1]
Citations Scopus - 2
2008 Brankovic L, Miller M, Steketee C, 'Special Collection: Privacy', Journal of Research and Practice in Information Technology, 40 149-150 (2008) [C3]
Co-authors Ljiljana Brankovic
2008 Brankovic L, Miller M, Steketee C, 'Special collection: Security', Journal of Research and Practice in Information Technology, 40 229-230 (2008) [C3]
Co-authors Ljiljana Brankovic
2008 Tang J, Miller M, Lin Y, 'HSAGA and its application for the construction of near-Moore digraphs', Journal of Discrete Algorithms, 6 73-84 (2008) [C1]
DOI 10.1016/j.jda.2007.05.003
Citations Scopus - 4
Co-authors Yuqing Lin
2008 Sugeng KA, Miller M, 'On consecutive edge magic total labeling of graphs', Journal of Discrete Algorithms (Amsterdam), 6 59-65 (2008) [C1]
DOI 10.1016/j.jda.2006.05.003
Citations Scopus - 6
2008 Iliopoulos C, Miller M, 'Special Issue of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) September 18-21, 2005, Ballarat, Australia', Journal of Discrete Algorithms (Amsterdam), 6 1-2 (2008) [C1]
DOI 10.1016/j.jda.2007.05.002
2008 Nguyen HM, Miller M, 'Structural properties of graphs of diameter 2 with maximal repeats', Discrete Mathematics, 308 2337-2341 (2008) [C1]
DOI 10.1016/j.disc.2006.09.057
2008 Lin Y, Balbuena C, Marcote X, Miller M, 'On the connectivity of (k, g)-cages of even girth', Discrete Mathematics, 308 3249-3256 (2008) [C1]
DOI 10.1016/j.disc.2007.06.030
Citations Scopus - 8Web of Science - 7
Co-authors Yuqing Lin
2008 Baskoro ET, Cholily YM, Miller M, 'Enumerations of vertex orders of almost Moore digraphs with selfrepeats', Discrete Mathematics, 308 123-128 (2008) [C1]
DOI 10.1016/j.disc.2007.03.035
Citations Scopus - 2Web of Science - 1
2008 Miller M, Simanjuntak R, 'Graphs of order two less than the Moore bound', Discrete Mathematics, 308 2810-2821 (2008) [C1]
DOI 10.1016/j.disc.2006.06.045
Citations Scopus - 1Web of Science - 1
2008 Nguyen MH, Miller M, 'Moore bound for mixed networks', Discrete Mathematics, 308 5499-5503 (2008) [C1]
DOI 10.1016/j.disc.2007.09.059
Citations Scopus - 2Web of Science - 1
2008 Balbuena C, Lin Y, Miller M, 'Diameter-sufficient conditions for a graph to be super-restricted connected', Discrete Applied Mathematics, 156 2827-2834 (2008) [C1]
DOI 10.1016/j.dam.2007.11.015
Citations Scopus - 4Web of Science - 4
Co-authors Yuqing Lin
2008 Miller M, Smyth B, 'Australasian Workshop on Combinatorial Algorithms - Foreword', FUNDAMENTA INFORMATICAE, 84 I-II (2008) [C3]
2008 Miller M, Smyth B, 'Australasian workshop on combinatorial algorithms (Special issue editorial)', Fundamenta Informaticae, 84 - (2008) [C2]
2008 Sueng KA, Miller M, Baca M, 'Super antimagic total labeling of graphs', Utilitas Mathematica, 76 161-171 (2008) [C1]
Citations Scopus - 1Web of Science - 1
2008 Baca M, Dafik, Miller M, 'Edge-antimagic total labeling of disjoint union of caterpillars', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 61-70 (2008) [C1]
Citations Scopus - 3
2008 Dafik, Miller M, Ryan J, Baca M, 'On antimagic labelings of disjoint union of complete s-partite graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 41-49 (2008) [C1]
Citations Scopus - 2
2008 Pineda-Villavicencio G, Miller M, 'On graphs of maximum degree 3 and defect 4', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 25-31 (2008) [C1]
Citations Scopus - 2
2008 Sugeng KA, Miller M, 'New constructions of A-magic graphs using labeling matrices', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 147-151 (2008) [C1]
2007 Baca M, Lin Y, 'Antimagic labelings of grids', Utilitas Mathematica, 72 65-75 (2007) [C1]
Citations Scopus - 8Web of Science - 6
Co-authors Yuqing Lin
2007 Balbuena C, Jiang T, Lin Y, Marcote X, Miller M, 'A lower bound on the order of regular graphs with given girth pair', Journal of Graph Theory, 55 153-163 (2007) [C1]
DOI 10.1002/jgt.20230
Citations Scopus - 7Web of Science - 3
Co-authors Yuqing Lin
2007 Hegde SM, Miller M, 'Further results on sequetially additive graphs', Discussiones Mathematicae: Graph Theory, 27 251-268 (2007) [C1]
2007 Baca M, Jendrol S, Miller M, Ryan J, 'On irregular total labellings', DISCRETE MATHEMATICS, 307 1378-1388 (2007) [C1]
DOI 10.1016/j.disc.2005.11.075
Citations Scopus - 67Web of Science - 37
2007 Nguyen HM, Miller M, Gimbert J, 'On mixed Moore graphs', Discrete Mathematics, 307 964-970 (2007) [C1]
DOI 10.1016/j.disc.2005.11.046
Citations Scopus - 5Web of Science - 3
2007 Baca M, Lin Y, Miller M, Youssef MZ, 'Edge-antimagic graphs', Discrete Mathematics, 307 1232-1244 (2007) [C1]
DOI 10.1016/j.disc.2005.10.038
Citations Scopus - 12Web of Science - 4
Co-authors Yuqing Lin
2007 Baca M, Jendrol S, Miller M, Ryan J, 'On irregular total labelings', Discrete Mathematics, 307 1378-1388 (2007) [C1]
DOI 10.1016/j.disc.2005.11.075
2006 Fiol MA, Gimbert J, Miller M, 'Multipartite Moore digraphs', LINEAR ALGEBRA AND ITS APPLICATIONS, 419 234-250 (2006) [C1]
DOI 10.1016/j.laa.2006.04.020
Citations Scopus - 3Web of Science - 3
2006 Marti JG, Miller M, 'Two new families of large compound graphs', NETWORKS, 47 140-146 (2006) [C1]
DOI 10.1002/net.20101
Citations Scopus - 2Web of Science - 2
2006 Lin Y, Miller M, Balbuena C, Marcote X, 'All (k;g)-Cages Are Edge-Superconnected', Networks, 47 102-110 (2006) [C1]
DOI 10.1002/net.20092
Citations Scopus - 9Web of Science - 9
Co-authors Yuqing Lin
2006 Sugeng KA, Miller M, 'Super edge-antimagic total labelings', UTILITAS MATHEMATICA, 71 131-141 (2006) [C1]
Citations Scopus - 6Web of Science - 4
2006 Sugeng KA, Miller M, Lin Y, Baca M, 'Face antimagic labelings of prisms', Utilitas Mathematica, 71 269-286 (2006) [C1]
Citations Scopus - 8Web of Science - 5
Co-authors Yuqing Lin
2006 Baca M, Lin Y, Miller M, Ryan JF, 'Antimagic labelings of Mobius grids', Ars Combinatoria, 78 3-13 (2006) [C1]
Citations Scopus - 2
Co-authors Yuqing Lin
2006 Miller M, Baca M, MacDougall JA, 'Vertex-magic Total Labeling of Generalized Petersen Graphs and Convex Polytopes', Journal of Combinatorial Mathematics and Combinatorial Computing, 59 89-99 (2006) [C1]
Co-authors Jim Macdougall
2006 Baca M, Baskoro ET, Miller M, Ryan J, Simanjuntak R, Sugeng KA, 'Survey of edge antimagic labelings of graphs', Majalah Ilmiah Himpunan Matematika Indonesia, 12 113-130 (2006) [C1]
2006 Koh KM, Miller M, Smyth WF, Wang Y, 'On optimum summable graphs', AKCE International Journal of Graphs and Combinatorics, 3 45-57 (2006) [C1]
2006 Baskoro ET, Cholily YM, Miller M, 'Structure of selfrepeat cycles in almost Moore digraphs with selfrepeats and diameter 3', Bulletin of the Institute of Combinatorics and its Applications, 46 99-109 (2006) [C1]
2006 Teska J, Ku¿el R, Miller M, 'Divisibility conditions in almost Moore digraphs with selfrepeats', Electronic Notes in Discrete Mathematics, 24 161-163 (2006) [C1]

Moore digraph is a digraph with maximum out-degree d, diameter k and order Md, k = 1 + d + ... + dk. Moore digraphs exist only in trivial cases if d = 1 (i.e., directed cycle Ck) ... [more]

Moore digraph is a digraph with maximum out-degree d, diameter k and order Md, k = 1 + d + ... + dk. Moore digraphs exist only in trivial cases if d = 1 (i.e., directed cycle Ck) or k = 1 (i.e., complete symmetric digraph). Almost Moore digraphs are digraphs of order one less than Moore bound. We shall present new properties of almost Moore digraphs with selfrepeats from which we prove nonexistence of almost Moore digraphs for some k and d. © 2006 Elsevier B.V. All rights reserved.

DOI 10.1016/j.endm.2006.06.043
Citations Scopus - 1
2006 Pineda-Villavicencio G, Gomez J, Miller M, Perez-Roses H, 'New largest graphs of diameter 6', Electronic Notes in Discrete Mathematics, 24 153-160 (2006) [C1]
DOI 10.1016/j.endm.2006.06.044
2006 Skinner GD, Miller M, Chang E, 'Managing privacy, trust, sercurity and context relationships using weighted graph representations', W S E A S Transactions on Information Science and Applications, 3 283-290 (2006) [C1]
Citations Scopus - 3
Co-authors Geoff Skinner
2006 Mishra V, Stranieri A, Miller M, Ryan J, 'Knowledge based regulation of statistical databases', WSEAS Transactions on Information Science and Applications, 3 239-244 (2006) [C1]

A statistical database system is a system that contains information about individuals, companies or organisations that enables authorized users to retrieve aggregate statistics su... [more]

A statistical database system is a system that contains information about individuals, companies or organisations that enables authorized users to retrieve aggregate statistics such as mean and count. The regulation of a statistical database involves limiting the use of the database so that no sequence of queries is sufficient to infer protected information about an individual. The database is said to be compromised when individual confidential information is obtained as a result of a statistical query. Devices to protect against compromise include adding noise to the data or restricting a query. While effective, these techniques are sometimes too strong in that legitimate compromises for reasons of public safety are always blocked. Further, a statistical database can be often be compromised with some knowledge about the database attributes (working knowledge), the real world (supplementary knowledge) or the legal system (legal knowledge). In this paper we illustrate that a knowledge based system that represents working, supplementary and legal knowledge can contribute to the regulation of a statistical database.

2006 Slamet S, Sugeng KA, Miller M, 'Sum graph based access structure in a secret sharing scheme', Journal of Prime Research in Mathematics, 2 113-119 (2006) [C1]
2006 Gimbert J, Lopez N, Miller M, Ryan J, 'Characterization of eccentric digraphs', DISCRETE MATHEMATICS, 306 210-219 (2006) [C1]
DOI 10.1016/j.disc.2005.11.015
Citations Scopus - 8Web of Science - 2
2006 Balbuena C, Barker E, Das KC, Lin Y, Miller M, Ryan J, et al., 'On the degrees of a strongly vertex-magic graph', Discrete Mathematics, 306 539-551 (2006) [C1]
DOI 10.1016/j.disc.2006.01.019
Citations Scopus - 11Web of Science - 7
Co-authors Yuqing Lin
2006 Balbuena C, Barker E, Lin Y, Miller M, Sugeng K, 'Consecutive magic graphs', Discrete Mathematics, 306 1817-1829 (2006) [C1]
DOI 10.1016/j.disc.2006.03.064
Citations Scopus - 2
Co-authors Yuqing Lin
2006 Gimbert J, Lopez N, Miller M, Ryan J, 'Characterization of eccentric graphs', Discrete Mathematics, 306 210-219 (2006) [C1]
DOI 10.1016/j.disc.2005.11.015
2005 Lin Y, Miller M, Balbuena C, 'Improved lower bound for the vertex connectivity of ([delta];g)-cages', Discrete Mathematics, 299 162-171 (2005) [C1]
DOI 10.1016/j.disc.2004.07.024
Citations Scopus - 13Web of Science - 12
Co-authors Yuqing Lin
2005 Baca M, Baskoro ET, Miller M, 'Antimagic valuations for the special class of plane graphs', COMBINATORIAL GEOMETRY AND GRAPH THEORY, 3330 58-64 (2005)
Citations Scopus - 3Web of Science - 1
2005 Tuga M, Miller M, 'd-Optimum exclusive sum labeling of certain graphs with radius one', Lecture Notes in Computer Science, 3330 216-225 (2005)

A mapping L is called a sum labeling of a graph H(V(H), E(H)) if it is an injection from V(H) to a set of positive integers, such that xy ¿E(H) if and only if there exists a vert... [more]

A mapping L is called a sum labeling of a graph H(V(H), E(H)) if it is an injection from V(H) to a set of positive integers, such that xy ¿E(H) if and only if there exists a vertex w ¿V(H) such that L(w) = L(x) + L(y). In this case, w is called a working vertex. We define L as an exclusive sum labeling of a graph G if it is a sum labeling of G¿K¯r for some non negative integer r, and G contains no working vertex. In general, a graph G will require some isolated vertices to be labeled exclusively. The least possible number of such isolated vertices is called exclusive sum number of G; denoted by e(G). An exclusive sum labeling of a graph G is said to be optimum if it labels G exclusively by using e(G) isolated vertices. In case e(G) = ¿(G), where ¿(G) denotes the maximum degree of vertices in G, the labeling is called ¿-optimum exclusive sum labeling. In this paper we present ¿-optimum exclusive sum labeling of certain graphs with radius one, that is, graphs which can be obtained by joining all vertices of an integral sum graph to another vertex. This class of graphs contains infinetely many graphs including some populer graphs such as wheels, fans, friendship graphs, generalised friendship graphs and multicone graphs. © Springer-Verlag Berlin Heidelberg 2005.

Citations Scopus - 1
2005 Baskoro ET, Miller M, Siran J, Sutton M, 'Complete Characterization of Almost Moore Digraphs of Degree Three', Journal of Graph Theory, 48 112-126 (2005) [C1]
DOI 10.1002/jgt.20042
Citations Scopus - 7Web of Science - 5
2005 Sugeng KA, Miller M, Lin Y, Baca M, 'Super (a,d)-vertex-antimagic labelings', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 91-102 (2005) [C1]
2005 Sugeng KA, Miller M, 'Relationship between adjacency matrices and super (a,d)-edge-antimagic total labeling', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 71-82 (2005) [C1]
2005 Miller M, Patel D, Ryan J, Sugeng KA, Slamin, Tuga M, 'Exclusive sum labeling of graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 137-148 (2005) [C1]
2005 Tuga M, Miller M, Ryan J, Ryjacek Z, 'Exclusive sum labelings of trees', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 109-121 (2005) [C1]
2005 Dahlhaus E, Manuel PD, Miller M, 'Parallel algorithms for generalized clique transversal problems', Australasian Journal of Combinatorics, 33 3-14 (2005) [C1]

For a hypergraph H(V,E), let = {Si,S2,...,Sr} be a family of subsets of V such that each St is a subset of some hyperedge of E. A -transversal problem is to find a minimum subfami... [more]

For a hypergraph H(V,E), let = {Si,S2,...,Sr} be a family of subsets of V such that each St is a subset of some hyperedge of E. A -transversal problem is to find a minimum subfamily of such that a hyperedge of H contains a member of whenever it contains a member of. This problem reduces to the transversal problem when = V and each St is a singleton set consisting of a vertex of V. The.FQ-dique transversal problem becomes a particular case of transversal problem when hyperedges are the maximal cliques and is the family of all cliques of size I. We give an NC-algorithm to solve-transversal problem on totally balanced hypergraphs. The main result of this paper is that the.fQ-clique transversal on strongly chordal graphs is solvable in polylogarithmic. time with polynomial number of processors.

2005 Lin Y, Miller M, Rodger C, 'All (k;g)-cages are k-edge-connected', Journal of Graph Theory, 48 219-227 (2005) [C1]
DOI 10.1002/jgt.20052
Citations Scopus - 10Web of Science - 9
Co-authors Yuqing Lin
2005 Gimbert J, Miller M, Ruskey F, Ryan J, 'Iterations of eccentric digraphs', Bulletin of the Institute of Combinatorics and its Applications, 45 41-50 (2005) [C1]
2005 Kelarev A, Miller M, Sokratova O, 'Languages recognized by two-sided automata of graphs', Proceedings of the Estonian Academy of Sciences, 54 46-54 (2005) [C1]
2005 Baca M, Baskoro ET, Cholily YM, Jendrol S, Lin Y, Miller M, et al., 'Conjectures and Open Problems on Face Antimagic Evaluations of Graphs', Journal of The Indonesian Mathematical Society, 11 175-192 (2005) [C1]
2004 Boland J, Buckley F, Miller M, 'Eccentric digraphs', DISCRETE MATHEMATICS, 286 25-29 (2004) [C1]
DOI 10.1016/j.disc.2003.11.041
Citations Scopus - 4Web of Science - 3
2004 Baca M, Baskoro ET, Jendrol S, Miller M, 'Antimagic labelings of hexagonal plane maps', UTILITAS MATHEMATICA, 66 231-238 (2004) [C1]
Citations Scopus - 8Web of Science - 6
2004 Baca M, Jendrol S, Miller M, Ryan J, 'Antimagic labelings of generalized Petersen graphs that are plane', ARS COMBINATORIA, 73 115-128 (2004) [C1]
Citations Scopus - 15Web of Science - 9
2004 Lin Y, Slamin, Baca M, Miller M, 'On d-antimagic labelings of prisms', ARS Combinatoria, 72 65-76 (2004) [C1]
Citations Scopus - 8Web of Science - 5
Co-authors Yuqing Lin
2004 Grosek O, Miller M, Ryan J, 'On non-polynomiality XOR over Z2, n', Tatra Mountains mathematical publications, 29 1-9 (2004) [C1]
2004 Skinner G, Chang E, McMahon M, Aisbett J, Miller M, 'Shield privacy hippocratic security method for virtual community', IECON Proceedings (Industrial Electronics Conference), 1 472-479 (2004)

Pearlman et al defines a virtual community as a large, multi-institutional group of individuals who use a set of rules, a policy, to specify how to share their resources. With suc... [more]

Pearlman et al defines a virtual community as a large, multi-institutional group of individuals who use a set of rules, a policy, to specify how to share their resources. With such a large collection of data stores in these resources, each of which could be data mined to different degrees, the privacy of each of the individuals needs to be protected. Within a virtual community, especially one also used to facilitate knowledge discovery, there are a number of privacy issues that must be addressed and resolved in ways other than through privacy laws and policies alone. This is due to the fact that, as to date, these laws have proved mainly ineffective and there is an ever growing concern by individuals about their privacy. Web surveys have identified that 82% of users have said improved privacy policies and methods would matter in web environments. Agarwal highlights the fact that a secure collaborative environment, such as a virtual community, needs to provide authentication, authorization, privacy and data integrity. In this paper, we identify the technology issues, followed by the presentation of our proposed solution. We provide a conceptual framework of the Hippocratic Security Method to provide information security for shield privacy in virtual communities and we describe the architecture and design of the proposed solution. We outline the implementation, testing and evaluation strategies of our solutions. The proposed solution shall monitor the use of personal information as it is passed around the virtual community and protected information paths, data at rest, database and information resources through the use of the hippocratic database principle to enforce hippocratic security policies and procedures together with privacy preserving data mining method for excellent information security in a virtual community environment. © 2004 IEEE.

DOI 10.1109/IECON.2004.1433355
Co-authors Geoff Skinner
2003 Lin Y, Slamin, Miller M, 'On d-antimagic labelings of antiprisms', Utilitas Mathematica, 64 213-220 (2003) [C1]
Citations Scopus - 1Web of Science - 1
Co-authors Yuqing Lin
2003 Miller M, Rodger C, Simanjuntak RMG, 'Distance magic labelings of graphs', Australasian Journal of Combinatorics, 28 305-315 (2003) [C1]
Citations Scopus - 17
2003 Baca M, Bertault FA, MacDougall JA, Miller M, Simanjuntak RMG, Slamin, 'Vertex-Antimagic total labelings of graphs', Discussiones Mathematicae Graph Theory, 23 67-83 (2003) [C1]
Co-authors Jim Macdougall
2002 Baca M, Miller M, Slamin, 'Vertex-Magic Total Labelings of Generalized Petersen Graphs', International Journal of Computer Mathematics, 79 1259-1263 (2002) [C1]
Citations Scopus - 14Web of Science - 8
2002 Brankovic L, Miller M, Siran J, 'On Range Query Usability of Statistical Databases', International Journal of Computer Mathematics, 79 1265-1271 (2002) [C1]
Co-authors Ljiljana Brankovic
2002 MacDougall JA, Miller M, Wallis W, Slamin, 'Vertex-Magic Total Labelings of Graphs', Utilitas Mathematica, 61 3-21 (2002) [C1]
Citations Scopus - 67Web of Science - 31
Co-authors Jim Macdougall
2002 Sutton M, Draganova A, Miller M, 'Mod sum number of wheels', ARS COMBINATORIA, 63 273-287 (2002)
Citations Scopus - 11Web of Science - 8
2002 Sutton M, Draganova A, Miller M, 'Mod Sum Number of Wheels', Arts Combinatoria, 63 1-15 (2002) [C1]
2002 Brankovic L, Horak P, Miller M, Rosa A, 'Premature Partial Latin Squares', Arts Combinatoria, 63 175-184 (2002) [C1]
Citations Scopus - 4Web of Science - 3
Co-authors Ljiljana Brankovic
2002 Baskoro ET, Surahmat, Nababan SM, Miller M, 'On Ramsey Numbers for Trees Versus Whels of Five or Six Vertices', Graphs and Combinatorics, 18 717-721 (2002) [C1]
Citations Scopus - 11Web of Science - 8
2002 MacDougall JA, Miller M, Wallis WD, 'Vertex-magic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175-183 (2002) [C1]
Citations Scopus - 17Web of Science - 5
Co-authors Jim Macdougall
2002 Slamin, Baca M, Lin Y, Miller M, Simanjuntak RMG, 'Edge-magic total labelings of wheels, fans and friendship graphs', Bulletin of the Institute of Combinatorics and its Applications, 35 89-98 (2002) [C1]
Co-authors Yuqing Lin
2001 Nagamochi H, Miller M, Slamin, 'Bounds on the number of isolates in sum graph labeling', Discrete Mathematics, 240 175-185 (2001) [C1]
Citations Web of Science - 2
2001 Miller M, Siran J, 'Diagraphs of degree two which miss the Moore bound by two', Discrete Mathematics, 226 269-280 (2001) [C1]
Citations Scopus - 4Web of Science - 2
2001 Sutton M, Miller M, 'On the sum number of wheels', Discrete mathematics, 232 185-188 (2001) [C1]
Citations Web of Science - 8
2001 Lin Y, Miller M, Simanjuntak RMG, Baca M, 'New constructions of magic and antimagic graph labelings', Utilitas Mathematica, 60 229-239 (2001) [C1]
Citations Web of Science - 29
Co-authors Yuqing Lin
2001 Baca M, Miller M, 'Antimagic Face Labeling of Convex Polytopes Based on Biprisms', The Journal of Combinatorial Mathematics and Combinatorial Computing, 36 229-236 (2001) [C1]
2001 Slamin, Miller M, 'On two conjectures concerning vertex-magic total labelings of generalized Petersen graphs', Bulletin of the Institute of Combinatorics and its Applications, 32 9-16 (2001) [C1]
2001 Lin Y, Miller M, 'Vertex magic total Labellings of complete graphs', Bulletin of the Institute of Combinatorics and its Applications, 33 68-76 (2001) [C1]
Co-authors Yuqing Lin
2000 Miller M, Gimbert J, Siran J, Slamin, 'Almost Moore digraphs are diregular', Discrete Mathematics, 218 265-270 (2000) [C1]
Citations Web of Science - 9
2000 Miller M, Dahlhaus E, Horak P, Ryan JF, 'The train marshalling problem', Discrete Applied Mathematics, 103 41-54 (2000) [C1]
Citations Web of Science - 21
2000 Miller M, Baskoro E, Plesnik J, 'Further results on almost Moore digraphs', ARS Combinatoria, 56 43-63 (2000) [C1]
Citations Scopus - 6Web of Science - 4
2000 Miller M, Brankovic L, Horak P, 'An Optimization Problem in Statistical Databases', SIAM Journal on Discrete Maths, 13, No 3 346-353 (2000) [C1]
Citations Scopus - 6Web of Science - 6
Co-authors Ljiljana Brankovic
2000 Miller M, Slamin, Wallis WD, Baskoro E, 'Edge-Magic total labelings', Australasian Journal of Combinatorics 22 (2000), 22 177-190 (2000) [C1]
Citations Scopus - 46
2000 Miller M, Baca M, 'Antimagic valuations of generalized Petersen graphs', The Australasian Jounrnal of Combinatorics, 22 135-139 (2000) [C1]
Citations Scopus - 10
2000 Baca M, MacDougall JA, Miller M, Wallis WD, Slamin, 'Survey of certain valuations of graphs', Discussiones Mathematicae: Graph Theory, 20 219-229 (2000) [C1]
Co-authors Jim Macdougall
2000 Miller M, Slamin, 'Diregularity of digraphs close to Moore bound', Journal of Indonesian Mathematical Society - MIHMI, 6 - No 5 185-192 (2000) [C1]
2000 Miller M, 'Open Problems in Graph Theory: Labelings and Extermal Graphs', Journal of Indonesian Mathematical Society - MIHMI, 6, No 5 165-178 (2000) [C1]
2000 Miller M, Simanjuntak RMG, 'A survey of (a,d)-antimagic graph labelings', Journal of Indonesian Mathematical Society - MIHMI, 6, N0 5 179-184 (2000) [C1]
2000 Slamin, Miller M, 'Sum Graph Labelling and Related Problems', MIHMI, 6, No 1 35-45 (2000) [C1]
1999 Sutton MJ, Miller M, Ryan JF, Slamin, 'Connected graphs which are not mod sum graphs', Discrete Math, 195 287-293 (1999) [C1]
Citations Scopus - 11Web of Science - 7
1999 Horak P, Brankovic L, Miller M, 'A Combinatorial problem in database security', Discrete Mathematics, 91 119-126 (1999) [C1]
Citations Scopus - 8Web of Science - 10
Co-authors Ljiljana Brankovic
1999 Miller M, Ryan JF, Slamin, 'Integral sum numbers of cocktail party graphs and symmetric complete bipartite graphs', Bulletin of ICA, 25 23-28 (1999) [C1]
1999 Sutton M, Miller M, 'Mod Sum Graph Labelling of Hm,n & Kn', The Australasian Journal of Combinatorics, 20 233-240 (1999) [C1]
Citations Scopus - 5
1999 Brankovic L, Miller M, Lieby P, 'Flattening Antichains with Respect to the Volume', The Electronic Journal of Combinatorics, Vol(6)1 * (1999) [C1]
Citations Scopus - 2
Co-authors Ljiljana Brankovic
1998 McKay BD, Miller M, Siran J, 'A note on large graphs of diameter two and given maximum degree', JOURNAL OF COMBINATORIAL THEORY SERIES B, 74 110-118 (1998)
DOI 10.1006/jctb.1998.1828
Citations Web of Science - 28
1998 Brankovic L, Miller M, Plesnik J, Ryan J, Siran J, 'large graphs with small degree and diameter: A voltage assignment approach', Australian Journal of Combinatorics, 18 65-76 (1998) [C1]
Citations Scopus - 5
Co-authors Ljiljana Brankovic
1998 Miller M, Ryan J, Smyth W, 'The Sum Number of the Cocktail Party Graph', Bulletin of the ICA, 22 79-90 (1998) [C1]
1998 Dahlhaus E, Manuel PD, Miller M, 'A characterization of strongly chordal graphs', Discrete Mathematics, 187 269-271 (1998) [C1]
Citations Scopus - 4Web of Science - 4
1998 Tri Baskoro E, Miller M, Plesnik J, 'On the Structure of Digraphs with Order Close to the Moore Bound', Graphs and Combinatorics, 14 109-119 (1998) [C1]
Citations Scopus - 15Web of Science - 11
1998 Dahlhaus E, Manuel PD, Miller M, 'Maximum h-colourable subgraph porblem in balanced graphs', Information Processing Letters, 65 301-303 (1998) [C1]
Citations Scopus - 21Web of Science - 16
1998 Miller M, Ryan JF, Smyth WF, Slamin, 'Labelling Wheels for Minimum Sum Number', Journal of Combinatorial Mathematics and Combinatorial Computing, 28 289-297 (1998) [C1]
1998 Kratochvil J, Manuel PD, Miller M, Proskurowski A, 'Disjoint and Unfolding Domination in Graphs', The Australasian Journal of Combinatorics, 18 277-292 (1998) [C1]
Citations Scopus - 1
1998 Brankovic L, Miller M, Plesnik J, Ryan J, Siran J, 'A note on constructing large Cayley graphs of given degree and diameter by voltage assignments', The Electronic Journal of Combinatorics, 5 1-11 (1998) [C1]
Citations Scopus - 11
Co-authors Ljiljana Brankovic
1996 Miller M, Cooper J, 'Security considerations for present and future medical databases', INTERNATIONAL JOURNAL OF BIO-MEDICAL COMPUTING, 41 39-46 (1996)
DOI 10.1016/0020-7101(95)01154-4
Citations Scopus - 5Web of Science - 7
1995 BASKORO ET, MILLER M, PLESNIK J, ZNAM S, 'DIGRAPHS OF DEGREE-3 AND ORDER CLOSE TO THE MOORE BOUND', JOURNAL OF GRAPH THEORY, 20 339-349 (1995)
DOI 10.1002/jgt.3190200310
Citations Web of Science - 13
1995 Morris S, Cooper J, Bomba D, Brankovic L, Miller M, Pacheco F, 'Australian Healthcare: Smart Card for a Clever Country', International Journal of Bio-Medical Computing, 40 101-105 (1995) [C1]
Citations Scopus - 3Web of Science - 2
Co-authors Ljiljana Brankovic
Show 177 more journal articles

Conference (71 outputs)

Year Citation Altmetrics Link
2013 Rylands L, Phanalasy O, Miller M, Ryan J, 'An application of completely separating systems to graph labeling', Combinatorial Algorithms: LNCS 8288, Rouen (2013) [E1]
DOI 10.1007/978-3-642-45278-9_32
Citations Scopus - 2
2013 Miller M, Baskoro ET, Slamin, Ryan J, 'Construction techniques for digraphs with minimum diameter', Combinatorial Algorithms: LNCS 8288, Rouen (2013) [E1]
DOI 10.1007/978-3-642-45278-9_28
2011 Phanalasy O, Miller M, Rylands L, Lieby P, 'On a relationship between completely separating systems and antimagic labeling of regular graphs', Combinatorial Algorithms, London, UK (2011) [E1]
DOI 10.1007/978-3-642-19222-7
Citations Scopus - 6Web of Science - 2
2011 Ryan JF, Phanalasy O, Miller M, Rylands L, 'On antimagic labeling for generalized web and flower graphs', Combinatorial Algorithms, London, UK (2011) [E1]
DOI 10.1007/978-3-642-19222-7_31
Citations Scopus - 4Web of Science - 1
2010 Bloom GS, Miller M, Manuel P, Rajan B, Rajasingh I, 'Star-labeled digraphs', Proceedings of the International Conference on Mathematics and Computer Science. ICMCS 2010, Chennai, India (2010) [E2]
2009 Fiala J, Kratochvil J, Miller M, 'Conference editors', Combinatorial Algorithms: 20th International Workshop, IWOCA 2009: Revised Selected Papers, Hradec nad Moravici, Czech Republic (2009) [E4]
2009 Iliopoulos CS, Miller M, Pissis SP, 'Parallel algorithms for degenerate and weighted sequences derived from high throughput sequencing technologies', Proceedings of the Prague Stringology Conference 2009, Prague, Czech Republic (2009) [E1]
Citations Scopus - 3
2008 Miller M, Nguyen MH, Pineda-Villavicencio G, 'On the non-existence of even degree graphs with diameter 2 and defect 2', Proceedings of the fourteenth symposium on Computing: the Australasian theory, Wollongong Australia (2008) [E1]
2008 Miller M, Wada K, 'Conference editors', IWOCA 2008: Proceedings of 19th International Workshop on Combinatorial Algorithms, Nagoya, Japan (2008) [E4]
2008 Miller M, Ryan J, Bu C, 'Proceedings of the Fourth International Workshop on Graph Labelings' (2008) [E4]
2008 Sugeng KA, Froncek D, Miller M, Ryan J, 'On distance magic labelings', Proceedings of the Fourth International Workshop on Graph Labelings, Harbin, China (2008) [E1]
2008 Tang J, Lin Y, Miller M, 'Construction of extremal graphs', IWOCA 2008: Proceedings of 19th International Workshop on Combinatorial Algorithms, Nagoya, Japan (2008) [E1]
Co-authors Yuqing Lin
2008 Miller M, 'Advances in the degree/diameter problem', Proceedings of the VIJMDA, Lleida, Spain (2008) [E1]
2007 Miller M, 'Security of Statistical Databases: Overview and Future Directions', In Proceedings of the Fifth Australasian Information Security Workshop (Privacy Enhancing Technologies), Ballarat (2007) [E3]
2007 Nguyen M, Miller M, Pineda-Villavicencio G, 'On the non-existence of odd degree graphs of diameter 2 and defect 2', Proceedings of the Eighteenth IWOCA Conference, Newcastle, Australia (2007) [E1]
2007 Dafik, Miller M, Iliopoulos C, Ryjacek Z, 'On diregularity of digraphs of defect two', Proceedings of the Eighteenth IWOCA Conference, Newcastle, Australia (2007) [E1]
2007 Tang J, Balbuena C, Lin Y, Miller M, 'An open problem: (4;g)-cages with odd g', Proceedings of the Thirteenth Computing: The Australasian Theory Symposium, Ballarat, Australia (2007) [E1]
2007 Marcote X, Balbuena C, Lin Y, Miller M, 'Un nuevo resultado sobre la conectividad de las jaulas con cintura par', Proceedings of Avances en Matematica Discreta en Andalucia, Andalusia, Spain (2007) [E1]
2006 Pineda-Villavicencio G, Miller M, 'On graphs of Maximum Degree 5, Diameter D and Defect 2', Journal of Combinatorial Mathematics and Combinatorial Computing, Mikulov, Czech Republic (2006) [E1]
2006 Pineda-Villavicencio G, Gómez J, Miller M, Pérez-Rosés H, 'New Largest Graphs of Diameter 6. (Extended Abstract)', Electronic Notes in Discrete Mathematics (2006) [E1]

In the pursuit of obtaining largest graphs of given degree and diameter, many construction techniques have arisen. Compounding of graphs is one such technique. In this paper, by m... [more]

In the pursuit of obtaining largest graphs of given degree and diameter, many construction techniques have arisen. Compounding of graphs is one such technique. In this paper, by means of the compounding of complete graphs into the bipartite Moore graph of diameter 6, we obtain two families of (¿, 6)-graphs. For maximum degree ¿ > 4, being ¿ - 1 a prime power, the members of these families constitute the largest known graphs of diameter 6. © 2006 Elsevier B.V. All rights reserved.

DOI 10.1016/j.endm.2006.06.044
2006 Rajasingh I, Rajan B, Manuel P, Miller M, 'Super edge-magic total labeling of spiked fans, hyper X-trees, dew drops and prisms', Proceedings of AWOCA 2006, the Seventeenth Australasian Workshop on Combinatorial Algorithms, Uluru, Australia (2006) [E1]
2006 Dafik, Miller M, Ryan J, Baca M, 'Super edge-antimagicness for a class of disconnected graphs', Proceedings of AWOCA 2006, the Seventeenth Australasian Workshop on Combinatorial Algorithms, Uluru, Australia (2006) [E1]
2006 Manuel P, Miller M, Rajan B, Rajasingh I, 'Cordial labeling of butterfly networks and mesh of trees', Proceedings of AWOCA 2006, the Seventeenth Australasian Workshop on Combinatorial Algorithms, Uluru, Australia (2006) [E1]
2006 Lin Y, Tang J, Brankovic L, Miller M, 'On graphs of maximum size with given girth', Proceedings of the Seventeenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2006), Uluru, NT (2006) [E1]
Co-authors Yuqing Lin, Ljiljana Brankovic
2005 Miller M, Nguyen MH, Simanjuntak R, 'Repeats in graphs and digraphs', Proceedings of AWOCA 2005, the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Australia (2005) [E1]
2005 Dafik, Miller M, Ryan J, Slamin, 'Open problems in the construction of large directed graphs', Proceedings of AWOCA 2005, the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Australia (2005) [E1]
2005 Sugeng K, Miller M, 'Properties of consecutive edge magic total graphs', Proceedings of AWOCA 2005, the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Australia (2005) [E1]
2005 Miller M, Pineda-Villavicencio G, 'On large graphs with given degree and diameter', Proceedings of AWOCA 2005, the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Australia (2005) [E1]
2005 Lin Y, Miller M, 'A Survey on the Connectivity of Cages', Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) : September 18-21, 2005 Ballarat, Australia, Ballarat, Vic. (2005) [E1]
Co-authors Yuqing Lin
2005 Tang J, Miller M, Lin Y, 'Hybrid Simulated Annealing and Genetic Algorithm for Degree/Diameter Problem', Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) : September 18-21, 2005 Ballarat, Australia, Ballarat, Vic. (2005) [E1]
Co-authors Yuqing Lin
2005 Tuga M, Miller M, 'Delta-Optimum exclusive sum labeling of certain graphs with radius one', Combinatorial Geometry and Graph Theory: Indonesia-Japan Joint Conference, IJCCGGT 2003 Bandung, Indonesia, September 13-16, 2003. Revised Selected Papers, Bandung, Indonesia (2005) [E1]
Citations Web of Science - 2
2005 Simanjuntak RMG, Miller M, 'Maximum order of planar digraphs', Combinatorial Geometry and Graph Theory: Indonesia-Japan Joint Conference, IJCCGGT 2003 Bandung, Indonesia, September 13-16, 2003. Revised Selected Papers, Bandung, Indonesia (2005) [E1]
2005 Sugeng KA, Miller M, Slamin, Baca M, '(a, d)-edge-antimagic Total labelings of caterpillars', Lecture Notes in Computer Science, Bandung, Indonesia (2005) [E1]
Citations Scopus - 20Web of Science - 14
2005 Skinner G, Miller M, 'Graph representation of access controls for managing privacy, trust, and security requirments', Proceedings of the 4th WSEAS International Conference on Information Security, Communications and Computers (ISCOCO 2005), Puerto De La Cruz, Tenerife, Canary Islands, Spain (2005) [E1]
2005 Baskoro ET, Miller M, 'Special Issue of the Sixteenth Australasian Workshop on Combinatorial Algorithms', Journal of Discrete Algorithms, Ballarat, Australia (2005) [E4]
2005 Patel D, Miller M, Patel KJ, 'On network securities and Internet vulnerabilities', Proceedings of IADIS International Conference on Applied Computing, Algarve, Portugal (2005) [E1]
2005 Mishra V, Stranieri A, Miller M, 'Context dependent security enforcement of statistical databases', Proceedings of the 4th WSEAS International Conference on Information Security, Communications and Computers (ISCOCO 2005), Puerto De La Cruz, Tenerife, Canary Islands, Spain (2005) [E1]
2005 Le Marshall B, Miller M, 'Privacy and e-health in Australia', Proceedings of the 4th WSEAS International Conference on Information Security, Communications and Computers (ISCOCO 2005), Puerto De La Cruz, Tenerife, Canary Islands, Spain (2005) [E1]
2004 Lin Y, Ahmad A, Miller M, Sugeng K, Baca M, 'Further results on d-antimagic labelings of antiprisms', Proceedings from Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina NSW, Aust (2004) [E1]
Co-authors Yuqing Lin
2004 Abeed A, Lin Y, Miller M, 'On d-antimagic labeling of biprisms and multiprisms', Proceedings of IWOGL 2004, Batu, Indonesia (2004) [E1]
2003 Miller M, Ryan JF, Slamin, Sugeng KA, Tuga M, 'Open Problems in Exclusive Sum Labeling', Proceeding for AWOCA 2003, Seoul, Korea (2003) [E1]
2003 Miller M, Ryan JF, Smyth WF, 'The Sum Number of a Disjoint Union of Graphs', Proceedings for AWOCA 2003, Seoul, Korea (2003) [E1]
2003 Miller M, Park K, 'Conference editor', Proceedings of the Fourteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2003, Seoul, Korea (2003) [E4]
2003 Chang E, Coleman C, Jayaratna N, Ye W, Miller M, 'Comparison of industry-sited projects and university-sited projects for final year students', Proceedings of the International Conference on Software Engineering Research and Practice, SERP '03, Las Vegas, NV (2003) [E1]
2002 Sugeng KA, Miller M, 'Open Problems in Secret Sharing', Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms, Queensland (2002) [E1]
2002 Lin Y, Miller M, 'Generalisations of Directed Moore Graphs', Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms, Queensland (2002) [E1]
Co-authors Yuqing Lin
2002 Miller M, Gimbert J, Ruskey F, Ryan J, 'Iterations of Eccentric Digraphs', Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms, Queensland (2002) [E1]
2002 Miller M, Nguyen HM, Slamin, 'Construction techniques for diregular and non-diregular large directed networks', Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms, Queensland (2002) [E1]
2002 Simanjuntak RMG, Miller M, 'Largest Planar Digraphs of Diamater Two', Proceedings of the Thirteenth Australasian Workshop on Combinatorial Algorithms, Queensland (2002) [E1]
2001 Kelarev A, Miller M, Sokratova O, 'Directed Graphs and Closure Properties for Languages', Proceedings of the Twelfth Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2001 Baca M, Miller M, Ryan J, 'On d-antimagic labelings of prisms and antiprisms', Proceedings of the Twelfth Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2001 Slamin, Tri Baskoro E, Miller M, 'Diregularity of digraphs of out-degree three and order two less than Moore bound', Proceedings of the Twelfth Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2001 Lin Y, Miller M, Rodger C, 'Edge-connectivity of cages', Proceedings of the Twelfth Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
Co-authors Yuqing Lin
2001 Kratochvil J, Miller M, Nguyen HM, 'Sum Graph labels - an Upper Bound and Related Problems', Proceedings of the Twelfth Australasian Workshop onCombinatorial Algorithms, Bandun, Indonesia (2001) [E1]
2001 Miller M, Rodger C, Simanjuntak RMG, 'On distance magic graphs', Proceedings of the Twelfth Australasian workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2001 Baca M, Tri Baskoro E, Miller M, 'On d-antimagic labelings of honeycomb', Proceedings of the Twelfth australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2001 Boland J, Miller M, 'The Eccentric Digraph of a Digraph', Proceedings of the Twelfth australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia (2001) [E1]
2000 Miller M, Slamin, 'On the Monotonicity of Minimum diameter with Respect to Order and Maximum Out-Degree', Computing and Combinatorics, 6th Annual International Conference, COCOON 2000, Bondi, Sydney, Australia (2000) [E1]
2000 Simanjuntak RMG, Miller M, Bertault FA, 'Two new (a,d)-antimagic graph labelings', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia (2000) [E1]
2000 Miller M, Baca M, Slamin, 'Every generalised Petersen graph has a vertex-magic total labeling', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia (2000) [E1]
2000 Lin Y, Miller M, Simanjuntak RMG, Slamin, 'Magic and antimagic labelings of wheels', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia (2000) [E1]
Co-authors Yuqing Lin
2000 Miller M, Sutton M, 'Using Graph Labellings to Store Linkages in Relational Databases', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW Australia (2000) [E1]
2000 Brankovic L, Miller M, Siran J, 'Usability of K-compromise free statistical databases', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia (2000) [E1]
Citations Scopus - 7
Co-authors Ljiljana Brankovic
2000 Baca M, Miller M, 'd-antimagic labelings of plane graphs', Proceedings of the Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia (2000) [E1]
2000 Dahlhaus E, Manne F, Miller M, Ryan J, 'Algorithms for Combinatorial Problems Related to Train Marshalling', Proceedings of the Eleventh Australasian Workshop on Combinatorial algorithms, Hunter Valley, NSW, Australia (2000) [E1]
1999 Miller M, MacDougall J, Slamin, Wallis W, 'Problems in Magic Total Graph Labellings', Combinatorial Algorithims -Proceedings of AWOCA'99, Perth (1999) [E1]
1999 Bertault FA, Miller M, 'An Algorithm for Drawing Compound Graphs', Lecture Notes in Computer Science - Graph Drawing, Stirin Castle, Czech Republic (1999) [E1]
Citations Web of Science - 6
1999 Bertault FA, Miller M, 'Extended Graph Model for Software Visualisation', Proceedings Software Visualisation workshop, Sydney, Australia (1999) [E1]
1999 Brankovic L, Miller M, 'The Spectrum of Premature Partial Latin Squares', Proceedings of the 10th Australian Workshop on Combinatorial, Perth, Western Australia (1999) [E1]
Co-authors Ljiljana Brankovic
1998 Brankovic L, Furche A, Miller M, Wrightson G, 'Newcash - Anonymous Digital Cash with Receipts', Proceedings of the 6th IEEE Singapore International Conference on Networks (SICON'98), Singapore (1998) [E1]
Co-authors Ljiljana Brankovic
1997 Dahlhaus E, Kratochvil J, Manuel PD, Miller M, 'Transversal partitioning in balanced hypergraphs', DISCRETE APPLIED MATHEMATICS, UNIV TWENTE, ENSCHEDE, NETHERLANDS (1997)
DOI 10.1016/S0166-218X(97)00034-6
Citations Scopus - 3Web of Science - 1
Show 68 more conferences
Edit

Grants and Funding

Summary

Number of grants 38
Total funding $343,688

Click on a grant title below to expand the full details for that specific grant.


20151 grants / $29,318

Graph Domination$29,318

Funding body: Kuwait University

Funding body Kuwait University
Project Team Mr Sudeep Stephen, Emeritus Professor Mirka Miller
Scheme Scholarship contribution
Role Lead
Funding Start 2015
Funding Finish 2015
GNo G1401351
Type Of Funding International - Non Competitive
Category 3IFB
UON Y

20123 grants / $51,000

Group Mission : Explore and analyse structures and properties of chemical compounds using computer assisted mathematics, combinatorics and graph theory.$35,000

Funding body: Department of Industry, Innovation, Science, Research and Tertiary Education

Funding body Department of Industry, Innovation, Science, Research and Tertiary Education
Project Team Doctor Yuqing Lin, Doctor Joe Ryan, Emeritus Professor Mirka Miller, Professor Ljiljana Brankovic, Professor Brian Alspach
Scheme Australia-China Science and Research Fund (ACSRF): Group Missions
Role Investigator
Funding Start 2012
Funding Finish 2012
GNo G1200258
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

2011 Awards for Supervision Excellence - VC and FEBE$12,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Award for Supervision Excellence
Role Lead
Funding Start 2012
Funding Finish 2012
GNo G1200055
Type Of Funding Internal
Category INTE
UON Y

2011 Awards for Supervision Excellence - Shared Account$4,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor Mike Calford, Associate Professor Jim Jose, Associate Professor Helen Warren-Forward, Doctor Keri Glastonbury, Emeritus Professor Mirka Miller, Doctor Geoffrey MacFarlane
Scheme Award for Supervision Excellence
Role Investigator
Funding Start 2012
Funding Finish 2012
GNo G1200057
Type Of Funding Internal
Category INTE
UON Y

20081 grants / $22,000

Networks, graphs and communications$22,000

Funding body: Department of Innovation, Industry, Science and Research

Funding body Department of Innovation, Industry, Science and Research
Project Team Emeritus Professor Mirka Miller, Professor Ljiljana Brankovic, Doctor Joe Ryan, Doctor Yuqing Lin
Scheme International Science Linkages Programme - French Australian Science and Technology Programme (FAST)
Role Lead
Funding Start 2008
Funding Finish 2008
GNo G0188626
Type Of Funding Other Public Sector - Commonwealth
Category 2OPC
UON Y

20041 grants / $3

Improving Upper and Lower Bounds on the Order of Large Graphs under Degree and Distance Constraints$3

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Emeritus Professor Mirka Miller
Scheme Discovery Projects
Role Lead
Funding Start 2004
Funding Finish 2004
GNo G0182975
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20036 grants / $55,343

Palladium based mobile agent system for collaborative environments$30,000

Funding body: Communication Electronics Solutions Pty Ltd

Funding body Communication Electronics Solutions Pty Ltd
Project Team Emeritus Professor Mirka Miller, Associate Professor Elizabeth Chang, Conjoint Professor Janet Aisbett
Scheme Linkage Projects Partner funding
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0182776
Type Of Funding Contract - Aust Non Government
Category 3AFC
UON Y

Magic and antimagic graph labellings.$10,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall, Emeritus Professor Mirka Miller
Scheme Project Grant
Role Investigator
Funding Start 2003
Funding Finish 2003
GNo G0182385
Type Of Funding Internal
Category INTE
UON Y

Broadcasting in resilient communication networks$7,103

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0182428
Type Of Funding Internal
Category INTE
UON Y

Visit of A/Prof J Gimbert Quintilla, from 7 October to 15 December 2003$4,740

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0183344
Type Of Funding Internal
Category INTE
UON Y

Cycles and Coloring, 2003, Slovakia 31 August - 5 September, 2003$2,500

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0183171
Type Of Funding Internal
Category INTE
UON Y

AWOGL '03 (Australasian Workshop on Graph Algorithms)$1,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Conference Establishment Grant
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0183553
Type Of Funding Internal
Category INTE
UON Y

20023 grants / $14,030

Graph labelings and their applications$6,714

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 2002
Funding Finish 2002
GNo G0181255
Type Of Funding Internal
Category INTE
UON Y

Visit of Prof Zdenek Ryjacek, from 1 July 2002 to 12 August 2002$4,816

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 2002
Funding Finish 2002
GNo G0181899
Type Of Funding Internal
Category INTE
UON Y

Cycles and Colorings 2002, Stara Lesna, Slovakia 8-13 September, 2002$2,500

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 2002
Funding Finish 2002
GNo G0182158
Type Of Funding Internal
Category INTE
UON Y

20015 grants / $70,554

Towards Improved Network Design Through the Study of Optimal Graphs$53,725

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Multi-Year Project Grant Scholarship
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0179977
Type Of Funding Internal
Category INTE
UON Y

Graph Labelings and Their Applications$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0179978
Type Of Funding Internal
Category INTE
UON Y

Towards Secure Computerized Systems Through the Study of Latin Squares$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller, Professor Ljiljana Brankovic
Scheme Project Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0179979
Type Of Funding Internal
Category INTE
UON Y

Visit of Prof Stanislav Jendrol from1 May 2001 to 16 July 2001$4,569

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0180804
Type Of Funding Internal
Category INTE
UON Y

American Mathematics Society Meeting, USA 16-18 March 2001$2,260

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0180701
Type Of Funding Internal
Category INTE
UON Y

20003 grants / $16,246

New Algorithims for Optimal Network Designs.$10,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Emeritus Professor Mirka Miller
Scheme Small Grant
Role Lead
Funding Start 2000
Funding Finish 2000
GNo G0178958
Type Of Funding Scheme excluded from IGS
Category EXCL
UON Y

A/Prof Martin Baca - 25July 2000 - 25 November 2000$5,348

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 2000
Funding Finish 2000
GNo G0179211
Type Of Funding Internal
Category INTE
UON Y

Komperenski Nasional X Matematika, Indonesia.$898

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 2000
Funding Finish 2000
GNo G0180315
Type Of Funding Internal
Category INTE
UON Y

19991 grants / $3,927

Visitor grant for A/Prof Baca$3,927

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 1999
Funding Finish 1999
GNo G0179001
Type Of Funding Internal
Category INTE
UON Y

19982 grants / $15,700

Constructions of Large Networks$9,500

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 1998
Funding Finish 1998
GNo G0177370
Type Of Funding Internal
Category INTE
UON Y

VIisit of Prof W Wallis 1/7-4/11/98$6,200

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller, Professor Walter Wallis
Scheme Visitor Grant
Role Lead
Funding Start 1998
Funding Finish 1998
GNo G0177721
Type Of Funding Internal
Category INTE
UON Y

19973 grants / $21,568

Optimal Directed Networks.$10,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Emeritus Professor Mirka Miller
Scheme Small Grant
Role Lead
Funding Start 1997
Funding Finish 1997
GNo G0176653
Type Of Funding Scheme excluded from IGS
Category EXCL
UON Y

Secure Statistical Databases for Electronic Payment Systems.$7,500

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Associate Professor Graham Wrightson, Emeritus Professor Mirka Miller
Scheme Project Grant
Role Investigator
Funding Start 1997
Funding Finish 1997
GNo G0176703
Type Of Funding Internal
Category INTE
UON Y

Miller - A/Prof Kratochvil - 18/10/97-20/12/97$4,068

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller, Assoc. Prof J Kratochvil
Scheme Visitor Grant
Role Lead
Funding Start 1997
Funding Finish 1997
GNo G0177509
Type Of Funding Internal
Category INTE
UON Y

19962 grants / $11,563

Large optimal directed networks.$7,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 1996
Funding Finish 1996
GNo G0175805
Type Of Funding Internal
Category INTE
UON Y

Visit by A/Prof J Siran. from 20/8/96 to 29/10/96$4,563

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 1996
Funding Finish 1996
GNo G0176357
Type Of Funding Internal
Category INTE
UON Y

19953 grants / $13,427

Construction of directed networks with minimum diameter$8,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 1995
Funding Finish 1995
GNo G0174967
Type Of Funding Internal
Category INTE
UON Y

Visit by A/Prof Jozef Siran, Associate Professor, Slovak Technical University, Bratislava, Slovakia. From 1/9/95 to 2/11/95 (9 weeks)$4,127

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 1995
Funding Finish 1995
GNo G0175628
Type Of Funding Internal
Category INTE
UON Y

10th Midwestern Conference on Combinatorics, Cryptography & Computing, Carbonvale USA, 19-21/10/95$1,300

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 1995
Funding Finish 1995
GNo G0175948
Type Of Funding Internal
Category INTE
UON Y

19942 grants / $10,475

Security subsystem for a database system$7,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 1994
Funding Finish 1994
GNo G0174756
Type Of Funding Internal
Category INTE
UON Y

Visit by Jan Kratochvil, Prague, 27 March 94 - 30 April 94.$3,475

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Visitor Grant
Role Lead
Funding Start 1994
Funding Finish 1994
GNo G0174592
Type Of Funding Internal
Category INTE
UON Y

19932 grants / $8,534

Optimal Directed Networks$7,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 1993
Funding Finish 1993
GNo G0172800
Type Of Funding Internal
Category INTE
UON Y

'International Conference on Combinatorics' - Keszthely, Hungary - 18 - 24 July 1993,'1st Slovak Workshop on Optimal Networks', Comenius Univ, 6 - 10 July 1993$1,534

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Emeritus Professor Mirka Miller
Scheme Travel Grant
Role Lead
Funding Start 1993
Funding Finish 1993
GNo G0174359
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Current Supervision

Commenced Research Title / Program / Supervisor Type
2015 Searching For Graphs That Are Close to The Moore Bound
Mathematics, Faculty of Science and Information Technology
Principal Supervisor
2014 Different Labelling Techniques for Graph Towards Application in Networking and Optimization
Mathematics, Faculty of Science and Information Technology
Principal Supervisor
2014 Conditional Resolvability of Graphs
Mathematics, Faculty of Science and Information Technology
Principal Supervisor
2014 Power Domination in Graphs
Mathematics, Faculty of Science and Information Technology
Principal Supervisor
2013 Extremal Graph Theory
Computer Science, Faculty of Engineering and Built Environment
Co-Supervisor

Past Supervision

Year Research Title / Program / Supervisor Type
2015 Large Interconnection Networks with Given Degree and Diameter
Computer Science, Faculty of Engineering and Built Environment
Co-Supervisor
2013 Antimagic Labeling of Graphs
Computer Science, Faculty of Engineering and Built Environment
Principal Supervisor
2012 Large Networks Bounded in Degree and Diameter
Computer Science, Faculty of Engineering and Built Environment
Principal Supervisor
2012 Extremal Networks and Connectivity
Computer Science, Faculty of Engineering and Built Environment
Principal Supervisor
2009 Variations of Classical Extremal Graph Theoretical Problems: Moore Bound and Connectivity
Computer Science, Faculty of Engineering and Built Environment
Principal Supervisor
2005 Interconnection Topologies for Low-Cost Networks
Computer Science, Faculty of Engineering and Built Environment
Sole Supervisor
2004 Topology and Fault Tolerance of Interconnection Networks
Computer Science, Faculty of Engineering and Built Environment
Sole Supervisor
2003 Distance-Related Problems in Graph Theory
Computer Science, Faculty of Engineering and Built Environment
Principal Supervisor
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Emeritus Professor Mirka Miller

Positions

Conjoint Professor
Director, GTA Research Group CARMA member
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Emeritus Professor
Director, GTA Research Group CARMA member
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email mirka.miller@newcastle.edu.au

Office

Room V214
Building Mathematics V
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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