2016 
Abawajy J, Kelarev AV, Miller M, Ryan J, 'Rees semigroups of digraphs for classification of data', Semigroup Forum, 92 121134 (2016)
Â© 2014, Springer Science+Business Media New York.Recent research has motivated the investigation of the weights of ideals in semiring constructions based on semigroups. The prese... [more]
Â© 2014, Springer Science+Business Media New York.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 S of the Rees semigroup of a digraph and for every zerodivisorfree idempotent semiring F with identity element, our main theorem describes all ideals J in the semigroup semiring F0[S] such that J has the largest possible weight.



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) [C1]
Â© 2014, University of Queensland. All rights reserved.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 to... [more]
Â© 2014, University of Queensland. All rights reserved.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.In this paper we deal with the problem of finding totally antimagic total labeling of some classes of graphs. We prove that paths, cycles, stars, doublestars and wheels are totally antimagic total. We also show that a union of regular totally antimagic total graphs is a totally antimagic total graph.



2015 
Holub P, Ryan JF, 'Degree diameter problem on triangular networks', Australasian Journal of Combinatorics, 63 333345 (2015) [C1] 


2015 
Baca M, Phanalasy O, Ryan J, SemanicovÃ¡FenovcÃkovÃ¡ A, 'Antimagic Labelings of Join Graphs', Mathematics in Computer Science, (2015) [C1]
An antimagic labeling of a graph with q edges is a bijection from the set of edges of the graph to the set of positive integers (Formula presented.) such that all vertex weights a... [more]
An antimagic labeling of a graph with q edges is a bijection from the set of edges of the graph to the set of positive integers (Formula presented.) such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. The join graph G + H of the graphs G and H is the graph with (Formula presented.) and (Formula presented.). The complete bipartite graph Km,n is an example of join graphs and we give an antimagic labeling for (Formula presented.). In this paper we also provide constructions of antimagic labelings of some complete multipartite graphs.



2015 
RIZVI STR, KHALID M, ALI K, MILLER M, RYAN J, 'ON CYCLESUPERMAGICNESS OF SUBDIVIDED GRAPHS', Bulletin of the Australian Mathematical Society, (2015) [C1]
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 
SemanicovÃ¡FenovcÃkovÃ¡ A, Baca M, LascsÃ¡kovÃ¡ M, Miller M, Ryan J, 'Wheels are CycleAntimagic', Electronic Notes in Discrete Mathematics, 48 1118 (2015) [C1]
Â© 2015 Elsevier B.V.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 admi... [more]
Â© 2015 Elsevier B.V.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 
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) [C1]
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 
Stephen S, Rajan B, Ryan J, Grigorious C, William A, 'Power domination in certain chemical structures', Journal of Discrete Algorithms, 33 1018 (2015) [C1]
Â© 2014 Elsevier B.V.Let G(V,E) be a simple connected graph. A set SÂ¿V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following th... [more]
Â© 2014 Elsevier B.V.Let G(V,E) be a simple connected graph. A set SÂ¿V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number ^{Â¿p}(G). In this paper, we establish a fundamental result that would provide a lower bound for the power domination number of a graph. Further, we solve the power domination problem in polyphenylene dendrimers, Rhenium Trioxide (ReO3) lattices and silicate networks.



2014 
FeriaPurÃ³n R, Ryan J, PÃ©rezRosÃ©s H, 'Searching for Large MultiLoop Networks', Electronic Notes in Discrete Mathematics, 46 233240 (2014) [C1]



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



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]



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 
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 
Arumugam S, Baca M, Froncek D, Ryan J, Sugeng KA, 'Some open problems on graph labelings', AKCE International Journal of Graphs and Combinatorics, 10 237243 (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.



2012 
Miller M, PÃ©rezRosÃ©s H, Ryan J, 'The Maximum DegreeandDiameterBounded Subgraph in the Mesh', CoRR, abs/1203.4069 (2012) 


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 
Sugeng KA, Ryan JF, 'Clique vertex magic cover of a graph', Mathematics in Computer Science, 5 113118 (2011) [C1]



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


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 
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]



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]



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 
Kelarev A, Ryan JF, Yearwood J, 'Cayley graphs as classifiers for data mining: The influence of asymmetries', Discrete Mathematics, 309 53605369 (2009) [C1]



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



2009 
Kelarev A, Ryan JF, Yearwood J, 'An algorithm for the optimization of multiple classifiers in data mining based on graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 71 6585 (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 
Ryan JF, 'Exclusive sum labeling of graphs: A survey', AKCE International Journal of Graphs and Combinatorics, 6 113126 (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 
Fernau H, Ryan J, Sugeng KA, 'A sum labelling for the generalised friendship graph', Discrete Mathematics, 308 734740 (2008) [C1]



2007 
Sugeng KA, Ryan J, 'On several classes of monographs', Australasian Journal of Combinatorics, 37 277284 (2007) [C1] 


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



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



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



2000 
Miller M, Dahlhaus E, Horak P, Ryan JF, 'The train marshalling problem', Discrete Applied Mathematics, 103 4154 (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 
Miller M, Ryan JF, Slamin, 'Integral sum numbers of cocktail party graphs and symmetric complete bipartite graphs', Bulletin of ICA, 25 2328 (1999) [C1] 


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 
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 
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]


