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 zerodivisorfree 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.



2015 
GÃ³mez J, Miller M, 'On the existence of radial Moore graphs for every radius and every degree', European Journal of Combinatorics, 47 1522 (2015)
The degree/diameter problem is to determine the largest graphs of given maximum degree and given diameter. General upper boundscalled Moore boundsfor 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 boundscalled Moore boundsfor 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.



2015 
Baca M, Miller M, Phanalasy O, Ryan J, SemanicovÃ¡FenovcÃkovÃ¡ A, Sillasen AA, 'Totally antimagic total graphs', Australasian Journal of Combinatorics, 61 4256 (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 edgeweight 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 edgeweight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertexweight 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 edgeantimagic total (vertexantimagic total) if all edgeweights (vertexweights) are pairwise distinct. If a labeling is simultaneously edgeantimagic total and vertexantimagic 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 105111 (2015)



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 215222 (2015) 


2015 
RIZVI STR, KHALID M, ALI K, MILLER M, RYAN J, 'ON CYCLESUPERMAGICNESS OF SUBDIVIDED GRAPHS', Bulletin of the Australian Mathematical Society, (2015)
LladÃ³ and Moragas [Â¿Cyclemagic graphsÂ¿, Discrete Math. 307 (2007), 2925Â¿2933] showed the cyclicmagic and cyclicsupermagic behaviour of several classes of connected graphs. ... [more]
LladÃ³ and Moragas [Â¿Cyclemagic graphsÂ¿, Discrete Math. 307 (2007), 2925Â¿2933] showed the cyclicmagic and cyclicsupermagic behaviour of several classes of connected graphs. They discussed cyclemagic labellings of subdivided wheels and friendship graphs, but there are no further results on cyclemagic labellings of other families of subdivided graphs. In this paper, we find cyclemagic 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 cyclesupermagic labellings for nonuniform subdivided fans and triangular ladders.



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 selfrepeats do not exist for infinitely many primes k.



2015 
SemanicovÃ¡FenovcÃkovÃ¡ A, Baca M, LascsÃ¡kovÃ¡ M, Miller M, Ryan J, 'Wheels are CycleAntimagic', Electronic Notes in Discrete Mathematics, 48 1118 (2015)
A simple graph G admits an Hcovering if every edge in E(G) belongs to a subgraph of G isomorphic to H. An (a, d)Hantimagic total labeling of a graph G admitting an Hcovering i... [more]
A simple graph G admits an Hcovering if every edge in E(G) belongs to a subgraph of G isomorphic to H. An (a, d)Hantimagic total labeling of a graph G admitting an Hcovering is a bijective function from the vertex set V(G) and the edge set E(G) of the graph G onto the set of integers {1, 2, ..., V(G)+E(G)} such that for all subgraphs H^{'} isomorphic to H, the sum of labels of all the edges and vertices belonging to H^{'} constitute the arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super cycleantimagic total labelings of wheel.



2015 
Miller M, Rajan RS, Parthiban N, Rajasingh I, 'Minimum Linear Arrangement of Incomplete Hypercubes', COMPUTER JOURNAL, 58 331337 (2015)



2015 
Abawajy J, Kelarev AV, Miller M, Ryan J, 'Distances of Centroid Sets in a GraphBased 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.



2015 
Miller M, Rajan B, Rajasingh I, 'Foreword', Mathematics in Computer Science, (2015)



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 353356 (2014) [C1]



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 4754 (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 wÂ¿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 wÂ¿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,Â±{1,2,...,j}),1=j= Â¿n/2Â¿,n=3, and for Harary graphs.



2014 
Holub P, Miller M, PerezRoses H, Ryan J, 'Degree diameter problem on honeycomb networks', DISCRETE APPLIED MATHEMATICS, 179 139151 (2014) [C1]



2014 
Conde J, Gimbert J, Gonzalez J, Miller M, Miret JM, 'On the nonexistence of almost Moore digraphs', EUROPEAN JOURNAL OF COMBINATORICS, 39 170177 (2014) [C1]



2014 
Christou M, Iliopoulos CS, Miller M, 'Maximizing the size of planar graphs under girth constraints', Journal of Combinatorial Mathematics and Combinatorial Computing, 89 129141 (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 Ctfree 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 SINICAENGLISH SERIES, 30 283290 (2014) [C1]



2014 
ABAWAJY J, KELAREV AV, MILLER M, RYAN J, 'Incidence Semirings of Graphs and Visible Bases', Bulletin of the Australian Mathematical Society, 89 451459 (2014) [C1]



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 4251 (2014) [C1]



2014 
Brankovic L, Lopez N, Miller M, Sebe F, 'Triangle randomization for social network data anonymization', Ars Mathematica Contemporanea, 7 461477 (2014) [C1]



2013 
FeriaPuron R, Miller M, PinedaVillavicencio G, 'On large bipartite graphs of diameter 3', DISCRETE MATHEMATICS, 313 381390 (2013) [C1]



2013 
Balbuena C, Miller M, Â¿irÃ¡n J, Â¿dÃmalovÃ¡ M, 'Large vertextransitive graphs of diameter 2 from incidence graphs of biaffine planes', Discrete Mathematics, 313 20142019 (2013) [C1]



2013 
Miller M, Ryan J, Ryjacek Z, Teska J, Vrana P, 'Stability of hereditary graph classes under closure operations', Journal of Graph Theory, 74 6780 (2013) [C1]



2013 
Marzuki CC, Salman ANM, Miller M, 'On the total irregularity strength of cycles and paths', Far East Journal of Mathematical Sciences, 82 121 (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 : VÂ¿E Â¿ {1, 2, ..., k} of a graph G is a totally irregular total klabeling 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 klabeling 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. Â© 2013 Pushpa Publishing House, Allahabad, India.



2013 
Christou M, Iliopoulos CS, Miller M, 'Degree/diameter problem for trees and pseudotrees', AKCE International Journal of Graphs and Combinatorics, 10 377389 (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 treelike 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 193198 (2013) [C1]



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 257272 (2013) [C1] 


2013 
Miller M, Ryan J, RyjÃ¡cek Z, 'Distancelocally disconnected graphs', Discussiones Mathematicae  Graph Theory, 33 203215 (2013) [C1]
For an integer k = 1, we say that a (finite simple undirected) graph G is kdistancelocally disconnected, or simply klocally disconnected if, for any x Â¿ V (G), the set of vert... [more]
For an integer k = 1, we say that a (finite simple undirected) graph G is kdistancelocally disconnected, or simply klocally disconnected if, for any x Â¿ 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 klocally 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.



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 315319 (2013) [C1]



2012 
Miller M, PÃ©rezRosÃ©s H, Ryan J, 'The Maximum DegreeandDiameterBounded 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 249259 (2012) [C1] 


2012 
Miller M, PerezRoses H, Ryan JF, 'The maximum degree and diameterbounded subgraph in the mesh', Discrete Applied Mathematics, 160 17821790 (2012) [C1]



2012 
Miller M, Phanalasy O, Ryan JF, Rylands L, 'Antimagicness of some families of generalized graphs', Australasian Journal of Combinatorics, 53 179190 (2012) [C1] 


2011 
Marshall KL, Miller M, Ryan JF, 'Extremal graphs without cycles of length 8 or less', Electronic Notes in Discrete Mathematics, 38 615620 (2011) [C2]



2011 
Miller M, Phanalasy O, Ryan JF, 'All graphs have antimagic total labelings', Electronic Notes in Discrete Mathematics, 38 645650 (2011) [C1]



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 8187 (2011) [C1] 


2011 
Miller M, Rajan B, Ryan JF, 'Foreword', Mathematics in Computer Science, 5 12 (2011) [C3] 


2011 
Feria Puron R, Miller M, PinedaVillavicencio G, 'On graphs of defect at most 2', Discrete Applied Mathematics, 159 13311344 (2011) [C1]



2011 
Loz E, Macaj M, Miller M, Siagiova J, Siran J, Tomanova J, 'Small vertextransitive and Cayley graphs of girth six and given degree: An algebraic approach', Journal of Graph Theory, 68 265284 (2011) [C1]



2011 
Dafik, Miller M, Ryan J, Baca M, 'Super edgeantimagic total labelings of mK,n,n', ARS COMBINATORIA, 101 97107 (2011) [C1]



2011 
Rylands L, Phanalasy O, Ryan JF, Miller M, 'Construction for antimagic generalized web graphs', AKCE International Journal of Graphs and Combinatorics, 8 141149 (2011) [C1]



2011 
Sugeng KA, Herawati BN, Miller M, Baca M, 'On magicness and antimagicness of the union of 4regular circulant graphs', Australasian Journal of Combinatorics, 50 141153 (2011) [C1] 


2011 
Miller M, 'Nonexistence of graphs with cyclic defect', Electronic Journal of Combinatorics, 18 15 (2011) [C1] 


2010 
Tang J, Lin Y, Miller M, 'New results on EX graphs', Mathematics in Computer Science, 3 119126 (2010) [C1]



2010 
Miller M, Wada K, 'Foreword', Mathematics in Computer Science, 3 12 (2010) [C3] 


2010 
Maryati TK, Salman ANM, Baskoro ET, Ryan JF, Miller M, 'On Hsupermagic labelings for certain shackles and amalgamations of a connected graph', Utilitas Mathematica, 83 333342 (2010) [C1]



2010 
Nguyen HM, Miller M, 'Structural properties of graphs of diameter 2 and defect 2', AKCE Journal of Graphs and Combinatronics, 7 2943 (2010) [C1] 


2010 
Baca M, Miller M, Phanalasy O, SemanicovaFenovcikova A, 'Super dantimagic labelings of disconnected plane graphs', Acta Mathematica Sinica, English Series, 26 22832294 (2010) [C1]



2009 
Delorme C, Flandrin E, Lin Y, Miller M, Ryan JF, 'On extremal graphs with bounded girth', Electronic Notes in Discrete Mathematics, 34 653657 (2009) [C2]



2009 
Miller M, Â¿irÃ¡n J, 'Moore graphs and beyond: A survey of the degree/diameter problem', Electronic Journal of Combinatorics, 161 (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 stateoftheart 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 Moorelike bounds for special types of graphs and digraphs, such as vertextransitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.



2009 
Dafik, Miller M, Ryan JF, Baca M, 'On super (a, d)edgeantimagic total labeling of disconnected graphs', Discrete Mathematics, 309 49094915 (2009) [C1]



2009 
PinedaVillavicencio G, Gomez J, Miller M, PerezRoses H, 'New largest known graphs of diameter 6', Networks, 53 315328 (2009) [C1]



2009 
Miller M, PinedaVillavicencio G, 'Complete catalogue of graphs of maximum degree 3 and defect at most 4', Discrete Applied Mathematics, 157 29832996 (2009) [C1]



2009 
Lin Y, Balbuena C, Miller M, 'On the number of components of (k, g)cages after vertex deletion', Discrete Applied Mathematics, 157 17601765 (2009) [C1]



2009 
Tang J, Lin Y, Balbuena C, Miller M, 'Calculating the extremal number ex (v ; {C3, C4, ..., Cn})', Discrete Applied Mathematics, 157 21982206 (2009) [C1]



2009 
Delorme C, Jorgensen LK, Miller M, PinedaVillavicencio G, 'On bipartite graphs of defect 2', European Journal of Combinatorics, 30 798808 (2009) [C1]



2009 
Baca M, Dafik, Miller M, Ryan J, 'Antimagic labeling of disjoint union of scrowns', Utilitas Mathematica, 79 193205 (2009) [C1]



2009 
Delorme C, Jorgensen LK, Miller M, PinedaVillavicencio G, 'On bipartite graphs of diameter 3 and defect 2', Journal of Graph Theory, 61 271288 (2009) [C1]



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 2137 (2009) [C1] 


2009 
Miller M, Nguyen MH, PinedaVillavicencio G, 'On the nonexistence of graphs of diameter 2 and defect 2', Journal of Combinatorial Mathematics and Combinatorial Computing, 71 520 (2009) [C1]



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 3948 (2009) [C1]



2009 
Arumugam S, Bloom GS, Miller M, Ryan JF, 'Some open problems on graph labelings', AKCE International Journal of Graphs and Combinatorics, 6 229236 (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 1932 (2009) [C1] 


2008 
Dafik, Miller M, Ryan JF, Baca M, 'Antimagic labeling of the union of two stars', The Australasian Journal of Combinatorics, 42 3544 (2008) [C1]



2008 
Brankovic L, Miller M, Steketee C, 'Special Collection: Privacy', Journal of Research and Practice in Information Technology, 40 149150 (2008) [C3]



2008 
Brankovic L, Miller M, Steketee C, 'Special collection: Security', Journal of Research and Practice in Information Technology, 40 229230 (2008) [C3]



2008 
Tang J, Miller M, Lin Y, 'HSAGA and its application for the construction of nearMoore digraphs', Journal of Discrete Algorithms, 6 7384 (2008) [C1]



2008 
Sugeng KA, Miller M, 'On consecutive edge magic total labeling of graphs', Journal of Discrete Algorithms (Amsterdam), 6 5965 (2008) [C1]



2008 
Iliopoulos C, Miller M, 'Special Issue of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005) September 1821, 2005, Ballarat, Australia', Journal of Discrete Algorithms (Amsterdam), 6 12 (2008) [C1]



2008 
Nguyen HM, Miller M, 'Structural properties of graphs of diameter 2 with maximal repeats', Discrete Mathematics, 308 23372341 (2008) [C1]



2008 
Lin Y, Balbuena C, Marcote X, Miller M, 'On the connectivity of (k, g)cages of even girth', Discrete Mathematics, 308 32493256 (2008) [C1]



2008 
Baskoro ET, Cholily YM, Miller M, 'Enumerations of vertex orders of almost Moore digraphs with selfrepeats', Discrete Mathematics, 308 123128 (2008) [C1]



2008 
Miller M, Simanjuntak R, 'Graphs of order two less than the Moore bound', Discrete Mathematics, 308 28102821 (2008) [C1]



2008 
Nguyen MH, Miller M, 'Moore bound for mixed networks', Discrete Mathematics, 308 54995503 (2008) [C1]



2008 
Balbuena C, Lin Y, Miller M, 'Diametersufficient conditions for a graph to be superrestricted connected', Discrete Applied Mathematics, 156 28272834 (2008) [C1]



2008 
Miller M, Smyth B, 'Australasian Workshop on Combinatorial Algorithms  Foreword', FUNDAMENTA INFORMATICAE, 84 III (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 161171 (2008) [C1]



2008 
Baca M, Dafik, Miller M, 'Edgeantimagic total labeling of disjoint union of caterpillars', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 6170 (2008) [C1]



2008 
Dafik, Miller M, Ryan J, Baca M, 'On antimagic labelings of disjoint union of complete spartite graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 4149 (2008) [C1]



2008 
PinedaVillavicencio G, Miller M, 'On graphs of maximum degree 3 and defect 4', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 2531 (2008) [C1]



2008 
Sugeng KA, Miller M, 'New constructions of Amagic graphs using labeling matrices', Journal of Combinatorial Mathematics and Combinatorial Computing, 65 147151 (2008) [C1] 


2007 
Baca M, Lin Y, 'Antimagic labelings of grids', Utilitas Mathematica, 72 6575 (2007) [C1]



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 153163 (2007) [C1]



2007 
Hegde SM, Miller M, 'Further results on sequetially additive graphs', Discussiones Mathematicae: Graph Theory, 27 251268 (2007) [C1] 


2007 
Baca M, Jendrol S, Miller M, Ryan J, 'On irregular total labellings', DISCRETE MATHEMATICS, 307 13781388 (2007) [C1]



2007 
Nguyen HM, Miller M, Gimbert J, 'On mixed Moore graphs', Discrete Mathematics, 307 964970 (2007) [C1]



2007 
Baca M, Lin Y, Miller M, Youssef MZ, 'Edgeantimagic graphs', Discrete Mathematics, 307 12321244 (2007) [C1]



2007 
Baca M, Jendrol S, Miller M, Ryan J, 'On irregular total labelings', Discrete Mathematics, 307 13781388 (2007) [C1]



2006 
Fiol MA, Gimbert J, Miller M, 'Multipartite Moore digraphs', LINEAR ALGEBRA AND ITS APPLICATIONS, 419 234250 (2006) [C1]



2006 
Marti JG, Miller M, 'Two new families of large compound graphs', NETWORKS, 47 140146 (2006) [C1]



2006 
Lin Y, Miller M, Balbuena C, Marcote X, 'All (k;g)Cages Are EdgeSuperconnected', Networks, 47 102110 (2006) [C1]



2006 
Sugeng KA, Miller M, 'Super edgeantimagic total labelings', UTILITAS MATHEMATICA, 71 131141 (2006) [C1]



2006 
Sugeng KA, Miller M, Lin Y, Baca M, 'Face antimagic labelings of prisms', Utilitas Mathematica, 71 269286 (2006) [C1]



2006 
Baca M, Lin Y, Miller M, Ryan JF, 'Antimagic labelings of Mobius grids', Ars Combinatoria, 78 313 (2006) [C1]



2006 
Miller M, Baca M, MacDougall JA, 'Vertexmagic Total Labeling of Generalized Petersen Graphs and Convex Polytopes', Journal of Combinatorial Mathematics and Combinatorial Computing, 59 8999 (2006) [C1]



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 113130 (2006) [C1] 


2006 
Koh KM, Miller M, Smyth WF, Wang Y, 'On optimum summable graphs', AKCE International Journal of Graphs and Combinatorics, 3 4557 (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 99109 (2006) [C1] 


2006 
Teska J, KuÂ¿el R, Miller M, 'Divisibility conditions in almost Moore digraphs with selfrepeats', Electronic Notes in Discrete Mathematics, 24 161163 (2006) [C1]
Moore digraph is a digraph with maximum outdegree 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 outdegree 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. Â© 2006 Elsevier B.V. All rights reserved.



2006 
PinedaVillavicencio G, Gomez J, Miller M, PerezRoses H, 'New largest graphs of diameter 6', Electronic Notes in Discrete Mathematics, 24 153160 (2006) [C1]



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 283290 (2006) [C1]



2006 
Mishra V, Stranieri A, Miller M, Ryan J, 'Knowledge based regulation of statistical databases', WSEAS Transactions on Information Science and Applications, 3 239244 (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 113119 (2006) [C1] 


2006 
Gimbert J, Lopez N, Miller M, Ryan J, 'Characterization of eccentric digraphs', DISCRETE MATHEMATICS, 306 210219 (2006) [C1]



2006 
Balbuena C, Barker E, Das KC, Lin Y, Miller M, Ryan J, et al., 'On the degrees of a strongly vertexmagic graph', Discrete Mathematics, 306 539551 (2006) [C1]



2006 
Balbuena C, Barker E, Lin Y, Miller M, Sugeng K, 'Consecutive magic graphs', Discrete Mathematics, 306 18171829 (2006) [C1]



2006 
Gimbert J, Lopez N, Miller M, Ryan J, 'Characterization of eccentric graphs', Discrete Mathematics, 306 210219 (2006) [C1]



2005 
Lin Y, Miller M, Balbuena C, 'Improved lower bound for the vertex connectivity of ([delta];g)cages', Discrete Mathematics, 299 162171 (2005) [C1]



2005 
Baca M, Baskoro ET, Miller M, 'Antimagic valuations for the special class of plane graphs', COMBINATORIAL GEOMETRY AND GRAPH THEORY, 3330 5864 (2005)



2005 
Tuga M, Miller M, 'dOptimum exclusive sum labeling of certain graphs with radius one', Lecture Notes in Computer Science, 3330 216225 (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 Â¿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 Â¿E(H) if and only if there exists a vertex w Â¿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 GÂ¿KÂ¯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) = Â¿(G), where Â¿(G) denotes the maximum degree of vertices in G, the labeling is called Â¿optimum exclusive sum labeling. In this paper we present Â¿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. Â© SpringerVerlag Berlin Heidelberg 2005.



2005 
Baskoro ET, Miller M, Siran J, Sutton M, 'Complete Characterization of Almost Moore Digraphs of Degree Three', Journal of Graph Theory, 48 112126 (2005) [C1]



2005 
Sugeng KA, Miller M, Lin Y, Baca M, 'Super (a,d)vertexantimagic labelings', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 91102 (2005) [C1] 


2005 
Sugeng KA, Miller M, 'Relationship between adjacency matrices and super (a,d)edgeantimagic total labeling', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 7182 (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 137148 (2005) [C1] 


2005 
Tuga M, Miller M, Ryan J, Ryjacek Z, 'Exclusive sum labelings of trees', Journal of Combinatorial Mathematics and Combinatorial Computing, 55 109121 (2005) [C1] 


2005 
Dahlhaus E, Manuel PD, Miller M, 'Parallel algorithms for generalized clique transversal problems', Australasian Journal of Combinatorics, 33 314 (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.FQdique 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 NCalgorithm to solvetransversal problem on totally balanced hypergraphs. The main result of this paper is that the.fQclique 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 kedgeconnected', Journal of Graph Theory, 48 219227 (2005) [C1]



2005 
Gimbert J, Miller M, Ruskey F, Ryan J, 'Iterations of eccentric digraphs', Bulletin of the Institute of Combinatorics and its Applications, 45 4150 (2005) [C1] 


2005 
Kelarev A, Miller M, Sokratova O, 'Languages recognized by twosided automata of graphs', Proceedings of the Estonian Academy of Sciences, 54 4654 (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 175192 (2005) [C1] 


2004 
Boland J, Buckley F, Miller M, 'Eccentric digraphs', DISCRETE MATHEMATICS, 286 2529 (2004) [C1]



2004 
Baca M, Baskoro ET, Jendrol S, Miller M, 'Antimagic labelings of hexagonal plane maps', UTILITAS MATHEMATICA, 66 231238 (2004) [C1]



2004 
Baca M, Jendrol S, Miller M, Ryan J, 'Antimagic labelings of generalized Petersen graphs that are plane', ARS COMBINATORIA, 73 115128 (2004) [C1]



2004 
Lin Y, Slamin, Baca M, Miller M, 'On dantimagic labelings of prisms', ARS Combinatoria, 72 6576 (2004) [C1]



2004 
Grosek O, Miller M, Ryan J, 'On nonpolynomiality XOR over Z2, n', Tatra Mountains mathematical publications, 29 19 (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 472479 (2004)
Pearlman et al defines a virtual community as a large, multiinstitutional 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, multiinstitutional 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. Â© 2004 IEEE.



2003 
Lin Y, Slamin, Miller M, 'On dantimagic labelings of antiprisms', Utilitas Mathematica, 64 213220 (2003) [C1]



2003 
Miller M, Rodger C, Simanjuntak RMG, 'Distance magic labelings of graphs', Australasian Journal of Combinatorics, 28 305315 (2003) [C1]



2003 
Baca M, Bertault FA, MacDougall JA, Miller M, Simanjuntak RMG, Slamin, 'VertexAntimagic total labelings of graphs', Discussiones Mathematicae Graph Theory, 23 6783 (2003) [C1]



2002 
Baca M, Miller M, Slamin, 'VertexMagic Total Labelings of Generalized Petersen Graphs', International Journal of Computer Mathematics, 79 12591263 (2002) [C1]



2002 
Brankovic L, Miller M, Siran J, 'On Range Query Usability of Statistical Databases', International Journal of Computer Mathematics, 79 12651271 (2002) [C1]



2002 
MacDougall JA, Miller M, Wallis W, Slamin, 'VertexMagic Total Labelings of Graphs', Utilitas Mathematica, 61 321 (2002) [C1]



2002 
Sutton M, Draganova A, Miller M, 'Mod sum number of wheels', ARS COMBINATORIA, 63 273287 (2002)



2002 
Sutton M, Draganova A, Miller M, 'Mod Sum Number of Wheels', Arts Combinatoria, 63 115 (2002) [C1] 


2002 
Brankovic L, Horak P, Miller M, Rosa A, 'Premature Partial Latin Squares', Arts Combinatoria, 63 175184 (2002) [C1]



2002 
Baskoro ET, Surahmat, Nababan SM, Miller M, 'On Ramsey Numbers for Trees Versus Whels of Five or Six Vertices', Graphs and Combinatorics, 18 717721 (2002) [C1]



2002 
MacDougall JA, Miller M, Wallis WD, 'Vertexmagic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175183 (2002) [C1]



2002 
Slamin, Baca M, Lin Y, Miller M, Simanjuntak RMG, 'Edgemagic total labelings of wheels, fans and friendship graphs', Bulletin of the Institute of Combinatorics and its Applications, 35 8998 (2002) [C1]



2001 
Nagamochi H, Miller M, Slamin, 'Bounds on the number of isolates in sum graph labeling', Discrete Mathematics, 240 175185 (2001) [C1]



2001 
Miller M, Siran J, 'Diagraphs of degree two which miss the Moore bound by two', Discrete Mathematics, 226 269280 (2001) [C1]



2001 
Sutton M, Miller M, 'On the sum number of wheels', Discrete mathematics, 232 185188 (2001) [C1]



2001 
Lin Y, Miller M, Simanjuntak RMG, Baca M, 'New constructions of magic and antimagic graph labelings', Utilitas Mathematica, 60 229239 (2001) [C1]



2001 
Baca M, Miller M, 'Antimagic Face Labeling of Convex Polytopes Based on Biprisms', The Journal of Combinatorial Mathematics and Combinatorial Computing, 36 229236 (2001) [C1] 


2001 
Slamin, Miller M, 'On two conjectures concerning vertexmagic total labelings of generalized Petersen graphs', Bulletin of the Institute of Combinatorics and its
Applications, 32 916 (2001) [C1] 


2001 
Lin Y, Miller M, 'Vertex magic total Labellings of complete graphs', Bulletin of the Institute of Combinatorics and its Applications, 33 6876 (2001) [C1]



2000 
Miller M, Gimbert J, Siran J, Slamin, 'Almost Moore digraphs are diregular', Discrete Mathematics, 218 265270 (2000) [C1]



2000 
Miller M, Dahlhaus E, Horak P, Ryan JF, 'The train marshalling problem', Discrete Applied Mathematics, 103 4154 (2000) [C1]



2000 
Miller M, Baskoro E, Plesnik J, 'Further results on almost Moore digraphs', ARS Combinatoria, 56 4363 (2000) [C1]



2000 
Miller M, Brankovic L, Horak P, 'An Optimization Problem in Statistical Databases', SIAM Journal on Discrete Maths, 13, No 3 346353 (2000) [C1]



2000 
Miller M, Slamin, Wallis WD, Baskoro E, 'EdgeMagic total labelings', Australasian Journal of Combinatorics 22 (2000), 22 177190 (2000) [C1]



2000 
Miller M, Baca M, 'Antimagic valuations of generalized Petersen graphs', The Australasian Jounrnal of Combinatorics, 22 135139 (2000) [C1]



2000 
Baca M, MacDougall JA, Miller M, Wallis WD, Slamin, 'Survey of certain valuations of graphs', Discussiones Mathematicae: Graph Theory, 20 219229 (2000) [C1]



2000 
Miller M, Slamin, 'Diregularity of digraphs close to Moore bound', Journal of Indonesian Mathematical Society  MIHMI, 6  No 5 185192 (2000) [C1] 


2000 
Miller M, 'Open Problems in Graph Theory: Labelings and Extermal Graphs', Journal of Indonesian Mathematical Society  MIHMI, 6, No 5 165178 (2000) [C1] 


2000 
Miller M, Simanjuntak RMG, 'A survey of (a,d)antimagic graph labelings', Journal of Indonesian Mathematical Society  MIHMI, 6, N0 5 179184 (2000) [C1] 


2000 
Slamin, Miller M, 'Sum Graph Labelling and Related Problems', MIHMI, 6, No 1 3545 (2000) [C1] 


1999 
Sutton MJ, Miller M, Ryan JF, Slamin, 'Connected graphs which are not mod sum graphs', Discrete Math, 195 287293 (1999) [C1]



1999 
Horak P, Brankovic L, Miller M, 'A Combinatorial problem in database security', Discrete Mathematics, 91 119126 (1999) [C1]



1999 
Miller M, Ryan JF, Slamin, 'Integral sum numbers of cocktail party graphs and symmetric complete bipartite graphs', Bulletin of ICA, 25 2328 (1999) [C1] 


1999 
Sutton M, Miller M, 'Mod Sum Graph Labelling of Hm,n & Kn', The Australasian Journal of Combinatorics, 20 233240 (1999) [C1]



1999 
Brankovic L, Miller M, Lieby P, 'Flattening Antichains with Respect to the Volume', The Electronic Journal of Combinatorics, Vol(6)1 * (1999) [C1]



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 110118 (1998)



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 6576 (1998) [C1]



1998 
Miller M, Ryan J, Smyth W, 'The Sum Number of the Cocktail Party Graph', Bulletin of the ICA, 22 7990 (1998) [C1] 


1998 
Dahlhaus E, Manuel PD, Miller M, 'A characterization of strongly chordal graphs', Discrete Mathematics, 187 269271 (1998) [C1]



1998 
Tri Baskoro E, Miller M, Plesnik J, 'On the Structure of Digraphs with Order Close to the Moore Bound', Graphs and Combinatorics, 14 109119 (1998) [C1]



1998 
Dahlhaus E, Manuel PD, Miller M, 'Maximum hcolourable subgraph porblem in balanced graphs', Information Processing Letters, 65 301303 (1998) [C1]



1998 
Miller M, Ryan JF, Smyth WF, Slamin, 'Labelling Wheels for Minimum Sum Number', Journal of Combinatorial Mathematics and Combinatorial Computing, 28 289297 (1998) [C1] 


1998 
Kratochvil J, Manuel PD, Miller M, Proskurowski A, 'Disjoint and Unfolding Domination in Graphs', The Australasian Journal of Combinatorics, 18 277292 (1998) [C1]



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, 5 111 (1998) [C1]



1996 
Miller M, Cooper J, 'Security considerations for present and future medical databases', INTERNATIONAL JOURNAL OF BIOMEDICAL COMPUTING, 41 3946 (1996)



1995 
BASKORO ET, MILLER M, PLESNIK J, ZNAM S, 'DIGRAPHS OF DEGREE3 AND ORDER CLOSE TO THE MOORE BOUND', JOURNAL OF GRAPH THEORY, 20 339349 (1995)



1995 
Morris S, Cooper J, Bomba D, Brankovic L, Miller M, Pacheco F, 'Australian Healthcare: Smart Card for a Clever Country', International Journal of BioMedical Computing, 40 101105 (1995) [C1]


