17Miller, Mirka
8Baca, Martin
7Dafik
7Sugeng, Kiki Ariyanti
4Slamin,
2Baskoro, Edy
2Jendrol, Stanislav
2Kelarev, Andrei
2Lin, Yuqing
2Marshall, Kim
2Mishra, Vivek
2Simanjuntak, Rinovia
2Stranieri, Andrew
2Tuga, Mauritsius
2Yearwood, John
1Balbuena, Camino
1Barker, Ewan
1Cholily, Yus Mochamad
1Das, K. C.

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130101 Pure Mathematics
50802 Computation Theory and Mathematics
3Graph theory
2Antimagic labeling
2Eccentricity
2Graphs
2Labeling
2Statistical database
2Sum graph
2Sum labelling
2Super (a,d)-edge-antimagic total labeling
1(A,d)-edge-antimagic total labeling
108 Information and Computing Sciences
1Cayley graphs
1Classification
1Classifiers
1Combinatorial algorithms
1Computational complexity
1Computational methods
1Construction techniques

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Format Type

A sum labelling for the generalised friendship graph

- Fernau, Henning, Ryan, Joe, Sugeng, Kiki Ariyanti

**Authors:**Fernau, Henning , Ryan, Joe , Sugeng, Kiki Ariyanti**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 5-6 (2008), p. 734-740**Full Text:**false**Reviewed:****Description:**We provide an optimal sum labelling scheme for the generalised friendship graph, also known as the flower (a symmetric collection of cycles meeting at a common vertex) and show that its sum number is 2. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

An algorithm for the optimization of multiple classifers in data mining based on graphs

- Kelarev, Andrei, Ryan, Joe, Yearwood, John

**Authors:**Kelarev, Andrei , Ryan, Joe , Yearwood, John**Date:**2009**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 65-85**Full Text:**false**Reviewed:****Description:**This article develops an efficient combinatorial algorithm based on labeled directed graphs and motivated by applications in data mining for designing multiple classifiers. Our method originates from the standard approach described in [37]. It defines a representation of a multiclass classifier in terms of several binary classifiers. We are using labeled graphs to introduce additional structure on the classifier. Representations of this sort are known to have serious advantages. An important property of these representations is their ability to correct errors of individual binary classifiers and produce correct combined output. For every representation like this we develop a combinatorial algorithm with quadratic running time to compute the largest number of errors of individual binary classifiers which can be corrected by the combined multiple classifier. In addition, we consider the question of optimizing the classifiers of this type and find all optimal representations for these multiple classifiers.**Description:**2003007563

Antimagic labeling of disjoint union of s-crowns

- Baca, Martin, Dafik, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Dafik , Miller, Mirka , Ryan, Joe**Date:**2009**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 79, no. (2009), p. 193-205**Full Text:**false**Reviewed:****Description:**A graph G is called (a, d)-edge-antimagic total if it admits a labeling of the vertices and edges by pairwise distinct integers of 1,2,..., |V(G)| + |E(G)| such that the edge-weights, w(uÏ…) = f(u) + f(Ï…) + f(uÏ…), uv âˆˆ E(G), form an arithmetic sequence with the first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. A construction of super (a, d)-edge-antimagic total labelings of some disconnected graphs are described.

Cayley graphs as classifiers for data mining : The influence of asymmetries

- Kelarev, Andrei, Ryan, Joe, Yearwood, John

**Authors:**Kelarev, Andrei , Ryan, Joe , Yearwood, John**Date:**2009**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 309, no. 17 (2009), p. 5360-5369**Relation:**http://purl.org/au-research/grants/arc/DP0211866**Full Text:****Reviewed:****Description:**The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids. Â© 2008 Elsevier B.V. All rights reserved.

**Authors:**Kelarev, Andrei , Ryan, Joe , Yearwood, John**Date:**2009**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 309, no. 17 (2009), p. 5360-5369**Relation:**http://purl.org/au-research/grants/arc/DP0211866**Full Text:****Reviewed:****Description:**The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids. Â© 2008 Elsevier B.V. All rights reserved.

Characterization of eccentric digraphs

- Gimbert, Joan, Lopez, Nacho, Miller, Mirka, Ryan, Joe

**Authors:**Gimbert, Joan , Lopez, Nacho , Miller, Mirka , Ryan, Joe**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 2 (2006), p. 210-219**Full Text:**false**Reviewed:****Description:**The eccentric digraph ED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G=ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement graph G is either self-centered of radius two or it is the union of complete graphs. As a consequence, we obtain that all trees except those with diameter 3 are eccentric digraphs. We also determine when ED(G) is symmetric in the cases when G is a graph or a digraph that is not strongly connected. Crown Copyright © 2006 Published by Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001601

Conjectures and open problems on face antimagic evaluations of graphs

- Miller, Mirka, Baca, Martin, Baskoro, Edy, Cholily, Yus Mochamad, Jendrol, Stanislav, Lin, Yuqing, Ryan, Joe, Simanjuntak, Rinovia, Slamin,, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Baca, Martin , Baskoro, Edy , Cholily, Yus Mochamad , Jendrol, Stanislav , Lin, Yuqing , Ryan, Joe , Simanjuntak, Rinovia , Slamin, , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Indonesian Mathematical Society MIHMI Vol. 11, no. 2 (2005), p. 175-192**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001408

Context-dependent security enforcement of statistical databases

- Ryan, Joe, Mishra, Vivek, Stranieri, Andrew, Miller, Mirka

**Authors:**Ryan, Joe , Mishra, Vivek , Stranieri, Andrew , Miller, Mirka**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the 4th WSEAS International Conference on Information Security, Communications and Computers, Tenerife, Spain, 16-18 December 2005, Tenerife, Spain : 16th December, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001390

**Authors:**Ryan, Joe , Mishra, Vivek , Stranieri, Andrew , Miller, Mirka**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the 4th WSEAS International Conference on Information Security, Communications and Computers, Tenerife, Spain, 16-18 December 2005, Tenerife, Spain : 16th December, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001390

Edge-antimagic total labeling of disjoint union of caterpillars

- Baca, Martin, Dafik, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Dafik , Miller, Mirka , Ryan, Joe**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 61-70**Full Text:**false**Reviewed:**

Exclusive sum labeling of graphs

- Miller, Mirka, Patel, Deval, Ryan, Joe, Sugeng, Kiki Ariyanti, Slamin,, Tuga, Mauritsius

**Authors:**Miller, Mirka , Patel, Deval , Ryan, Joe , Sugeng, Kiki Ariyanti , Slamin, , Tuga, Mauritsius**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 137-148**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001402

Exclusive sum labelings of trees

- Miller, Mirka, Tuga, Mauritsius, Ryan, Joe, Ryjacek, Zdenek

**Authors:**Miller, Mirka , Tuga, Mauritsius , Ryan, Joe , Ryjacek, Zdenek**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 109-121**Full Text:**false**Reviewed:****Description:**The notions of**Description:**C1**Description:**2003001406

Knowledge based regulation of statistical databases

- Mishra, Vivek, Stranieri, Andrew, Miller, Mirka, Ryan, Joe

**Authors:**Mishra, Vivek , Stranieri, Andrew , Miller, Mirka , Ryan, Joe**Date:**2006**Type:**Text , Journal article**Relation:**WSEAS Transactions on Information Science and Applications Vol. 3, no. 2 (2006), p. 239-244**Full Text:**false**Reviewed:****Description:**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.**Description:**C1**Description:**2003001608

Mode and antimode graphs

**Authors:**Ryan, Joe , Marshall, Kim**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001389

**Authors:**Ryan, Joe , Marshall, Kim**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005**Full Text:****Reviewed:****Description:**E1**Description:**2003001389

On antimagic labelings of disjoint union of complete s-partite graphs

- Dafik, Miller, Mirka, Ryan, Joe, Baca, Martin

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

**Authors:**Marshall, Kim , Ryan, Joe**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 65, no. (May 2008 2008), p. 51-60**Full Text:**false**Reviewed:****Description:**The term mode graph was introduced by Boland, Kauffman and Panroug [2] to defiue a connected graph G such that, for every pair of vertices v, w in G, the number of vertices with eccentricity e(v) is equal to the number of vertices with eccentricity e(w). As a natural extension to this work, the concept of an antimode graph was introduced to describe a graph for which if e(v) ≠ e(w) then the number of vertices with eccentricity e(v) is not equal to the number of vertices with eccentricity e(w). ln this paper we determine the existence of some classes of antimode graphs, namely equisequential and (a, d)-antimode graphs.

On irregular total labellings

- Baca, Martin, Jendrol, Stanislav, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

On non-polynomiality of XOR over Zn2

- Grosek, Otokar, Miller, Mirka, Ryan, Joe

**Authors:**Grosek, Otokar , Miller, Mirka , Ryan, Joe**Date:**2004**Type:**Text , Journal article**Relation:**Tatra Mountains Mathematical Publications Vol. 29, no. (2004), p. 183-191**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000905

On several classes of monographs

- Sugeng, Kiki Ariyanti, Ryan, Joe

**Authors:**Sugeng, Kiki Ariyanti , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Australasian Journal of Combinatorics Vol. 37, no. (2007), p. 277-284**Full Text:**false**Reviewed:****Description:**C1**Description:**2003004943

On the degrees of a strongly vertex-magic graph

- Balbuena, Camino, Barker, Ewan, Das, K. C., Lin, Yuqing, Miller, Mirka, Ryan, Joe, Slamin,, Sugeng, Kiki Ariyanti, Tkac, M.

**Authors:**Balbuena, Camino , Barker, Ewan , Das, K. C. , Lin, Yuqing , Miller, Mirka , Ryan, Joe , Slamin, , Sugeng, Kiki Ariyanti , Tkac, M.**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 6 (2006), p. 539-551**Full Text:**false**Reviewed:****Description:**Let G=(V,E) be a finite graph, where |V|=n≥2 and |E|=e≥1. A vertex-magic total labeling is a bijection λ from V∪E to the set of consecutive integers {1,2,...,n+e} with the property that for every v∈V, λ(v)+∑w∈N(v)λ(vw)=h for some constant h. Such a labeling is strong if λ(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e≥10n2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs. © 2006 Elsevier B.V. All rights reserved**Description:**C1**Description:**2003001603

Open problems in the construction of large directed graphs

- Dafik, Miller, Mirka, Ryan, Joe, Slamin,

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Slamin,**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Victoria : 18th - 21st September, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001352

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