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20Lin, Yuqing
19Baca, Martin
19Sugeng, Kiki Ariyanti
17Ryan, Joe
9Pineda-Villavicencio, Guillermo
8Balbuena, Camino
7Baskoro, Edy
6Dafik
6Slamin,
5Nguyen, Minh Hoang
5Tang, Jianmin
4Cholily, Yus Mochamad
4Simanjuntak, Rinovia
3Gimbert, Joan
3Manuel, Paul
3Marcote, Xavier
3Skinner, Geoff
3Tuga, Mauritsius
2Ahmad, Abeed

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460101 Pure Mathematics
14Graph theory
110802 Computation Theory and Mathematics
9Antimagic labeling
8Degree/diameter problem
8Moore bound
6Connectivity
50103 Numerical and Computational Mathematics
5Diameter
5Digraphs
5Graph
5Graphs
5Numerical methods
5Security
4Moore graphs
4Number theory
4Set theory
4Sum labelling
4Theorem proving
308 Information and Computing Sciences

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Hybrid simulated annealing and genetic algorithm for degree/diameter problem

- Tang, Jianmin, Miller, Mirka, Lin, Yuqing

**Authors:**Tang, Jianmin , Miller, Mirka , Lin, Yuqing**Date:**2005**Type:**Text , Conference paper**Relation:**Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 321-331**Full Text:**false**Description:**The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. This paper deals with directed graphs. General upper bounds, called Moore bounds, exist for the largest possible order of such digraphs of maximum degree d and diameter k. It is known that simulated annealing and genetic algorithm are effective techniques to identify global optimization solutions. This paper describes our attempt to build a Hybrid Simulated Annealing and Genetic Algorithm (HSAGA) that can be used to construct larger digraphs, and displays our preliminary results obtained by HSAGA.**Description:**2003001438

Super edge-antimagic total labelings of mKn,n,n

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

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2011**Type:**Text , Journal article**Relation:**Ars Combinatoria Vol. 101, no. (2011), p. 97-107**Full Text:**false**Reviewed:****Description:**An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V(G) ∪ E(G) onto the integers 1,2,...,p + q with the property that the edge-weights, w(uv) = f(u)+f(v)+f(uv) where uv Îµ E(G), form an arithmetic progression starting from a and having 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 (a, d)-edge-antimagic total labeling of disjoint union of multiple copies of complete tripartite graph and disjoint union of stars.**Description:**An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V(G) ∪ E(G) onto the integers 1,2,...,p + q with the property that the edge-weights, w(uv) = f(u)+f(v)+f(uv) where uv Îµ E(G), form an arithmetic progression starting from a and having 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 (a, d)-edge-antimagic total labeling of disjoint union of multiple copies of complete tripartite graph and disjoint union of stars.

Privacy and e-health in Australia

- Miller, Mirka, Le Marshall, Bruce

**Authors:**Miller, Mirka , Le Marshall, Bruce**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the 4th WSEAS International Conference on Information Security, Communications and Computers, Tenerife, Spain : 16th -18th December, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001395

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

On network security and internet vulnerability

- Miller, Mirka, Patel, Deval, Patel, Keyurkumar

**Authors:**Miller, Mirka , Patel, Deval , Patel, Keyurkumar**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at IADIS International Conference on Applied Computing 2005, Volume II, Algarve, Portugal : 22nd - 25th February, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001409

Parallel algorithms for generalized clique transversal problems

- Miller, Mirka, Dahlhaus, Elias, Manuel, Paul

**Authors:**Miller, Mirka , Dahlhaus, Elias , Manuel, Paul**Date:**2005**Type:**Text , Journal article**Relation:**Australasian Journal of Combinatorics Vol. 33, no. (2005), p. 3-14**Full Text:**false**Reviewed:****Description:**The K ` - clique transversal problem is to locate a minimum collection of cliques of size ` in a graph G such that every maximal clique of size ` in G contains at least one member of the collection. We give an NC algorithm to solve this problem on strongly chordal graphs. Keywords: balanced graphs, strongly chordal graphs, clique transversal, k-fold clique transversal, K ` - clique transversal. 1 Introduction A 0 Gamma 1 matrix is balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of an odd cycle. A 0 Gamma 1 matrix is totally balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of any cycle. A hypergraph H is an ordered pair (V; E) where V is a set of vertices and E is a family of subsets of V . The members of E are called hyperedges of H . Let V = fv 1 ; v 2 ; : : : ; v n g and E = fE 1 ; E 2 ; : : : ; Em g. Let A(H) denote the hyperedge - vertex incidence matrix of a hypergraph H .**Description:**C1**Description:**2003001400

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:**

Further results in d-antimagic labelings of antiprisms

- Lin, Yuqing, Ahmad, Abeed, Miller, Mirka, Sugeng, Kiki Ariyanti, Baca, Martin

**Authors:**Lin, Yuqing , Ahmad, Abeed , Miller, Mirka , Sugeng, Kiki Ariyanti , Baca, Martin**Date:**2004**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2004: Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina, New South Wales : 6-9th July, 2004**Full Text:**false**Reviewed:****Description:**E1**Description:**2003000900

Super antimagic total labeling of graphs

- Sugeng, Kiki Ariyanti, Miller, Mirka, Baca, Martin

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 76, no. (2008), p. 161-171**Full Text:**false**Reviewed:****Description:**Let G = (V, E) be a simple, finite and undirected graph with v vertices and e edges, A graph labeling is a mapping from elements of a graph to a set of numbers (usually positive integers). If the domain of the mapping is the set of vertices (or edges) then the labeling is called vertex-labeling (or edge-labeling). If the domain of the mapping is the set of vertices and edges then the labeling is called total labeling. The sum of all labels associated with a graph element is called the weight of the element. If the weights of vertices (or the weights of edges) form an arithmetic progression starting at a and with difference d, then the labeling is called (a, d)-vertex-antimagic (or (a, d)-edge-antimagic). Such a labeling is called v-super (or e-super) if the smallest labels appear on the vertices (or edges). In this paper we present new results for v-super vertex-antimagic total and e-super edge-antimagic total labeling.**Description:**C1

Super edge-antimagicness for a class of disconnected graphs

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

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2006**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2006, 17th Australasian Workshop on Combinatorial Algorithms, Uluru, Australia : 13th July, 2006 p. 67-75**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001916

New constructions of A-magic graphs using labeling matrices

- Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 147-151**Full Text:**false**Reviewed:**

On the structure of (d,3)-digraphs containing selfrepeats

- Baskoro, Edy, Cholily, Yus Mochamad, Miller, Mirka

**Authors:**Baskoro, Edy , Cholily, Yus Mochamad , Miller, Mirka**Date:**2004**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2004: Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina, New South Wales : 6-9th July, 2004**Full Text:**false**Reviewed:****Description:**E1**Description:**2003000901

- Baca, Martin, Lin, Yuqing, Miller, Mirka

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 72, no. (2007), p. 65-75**Full Text:**false**Reviewed:****Description:**In this paper we deal with the problem of labeling the vertices, edges and faces of a grid graph by the consecutive integers from 1 to |V| + |E| + |F| in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face weights then form an arithmetic progression with common difference d.**Description:**C1**Description:**2003004808

Super vertex-magic total labelings of graphs

- MacDougall, James, Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**MacDougall, James , Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2004**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2004: Fifteenth Australasian Workshop on Combinatorial Algorithms, Ballina, New South Wales : 6th - 9th July, 2004 p. 222–229**Full Text:**false**Reviewed:****Description:**E1**Description:**2003000902

On the nonexistence of graphs of diameter 2 and defect 2

- Miller, Mirka, Nguyen, Minh Hoang, Pineda-Villavicencio, Guillermo

**Authors:**Miller, Mirka , Nguyen, Minh Hoang , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 5-20**Full Text:**false**Reviewed:****Description:**In 1960, Hoffman and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d² + 1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdös et al., using eigenvalue analysis, showed that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d² vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d² - 1 vertices do not exist for most values of d with d ≥ 6, and conjecture that they do not exist for any d ≥ 6.**Description:**2003007893

Moore graphs and beyond : A survey of the degree/diameter problem

**Authors:**Miller, Mirka , Siran, Jozef**Date:**2005**Type:**Text , Journal article**Relation:**Electronic Journal of Combinatorics Vol. DS14, no. (2005), p. 1-61**Full Text:**false**Reviewed:****Description:**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 maximum possible number of vertices, given the other two parameters, and thus attacking 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.**Description:**C1**Description:**2003001407

Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2005)

- Ryan, Joe, Manyem, Prabhu, Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Ryan, Joe , Manyem, Prabhu , Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2005**Type:**Text , Conference proceedings**Full Text:**false

Super edge-antimagic total labeling

- Sugeng, Kiki Ariyanti, Miller, Mirka, Baca, Martin

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2006**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 71, no. (2006), p. 131-141**Full Text:**false**Reviewed:****Description:**A (p, q)-graph G is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1,2,...,p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Moreover, G is said to be super (a, d)-edge-antimagic total if f(V(G)) = {1,2,..., p}. In this paper we study the super (a,d)-edge-antimagic total properties of certain classes of graphs, including ladders, generalized prisms and antiprisrns.**Description:**C1**Description:**2003001596

On graphs of maximum degree 3 and defect 4

- Pineda-Villavicencio, Guillermo, Miller, Mirka

**Authors:**Pineda-Villavicencio, Guillermo , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 25-31**Full Text:**false**Reviewed:****Description:**It is well known that apart from the Petersen graph there are no Moore graphs of degree 3. As a cubic graph must have an even number of vertices, there are no graphs of maximum degree 3 and

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

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