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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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(a,d)-edge-antimagic total labelings of caterpillars

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

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Slamin, , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**Combinatorial Geometry and Graph Theory, LNCS 3330, Lecture Notes in Computer Science, Indonesia-Japan Joint Conference IJCCGGT 2003, Bandung, Indonesia, September 2003, Revised Selected Papers Vol. 3330, no. (2005), p. 169-180**Full Text:**false**Reviewed:****Description:**For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .**Description:**C1**Description:**2003001412

A lower bound on the order of regular graphs with given girth pair

- Balbuena, Camino, Jiang, T., Lin, Yuqing, Marcote, Xavier, Miller, Mirka

**Authors:**Balbuena, Camino , Jiang, T. , Lin, Yuqing , Marcote, Xavier , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 55, no. 2 (2007), p. 153-163**Full Text:**false**Reviewed:****Description:**The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209-218]. A (**Description:**C1**Description:**2003004727

A survey on the connectivity of cages

**Authors:**Miller, Mirka , Lin, Yuqing**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at the Sixteenth Australasian Workshop on Combinatorial Algorithms, 18-21 September 2005, Ballarat, Australia, Ballarat, Victoria : 18th -21st September, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001393

All (k;g)-cages are edge-superconnected

- Lin, Yuqing, Miller, Mirka, Balbuena, Camino, Marcote, Xavier

**Authors:**Lin, Yuqing , Miller, Mirka , Balbuena, Camino , Marcote, Xavier**Date:**2006**Type:**Text , Journal article**Relation:**Networks Vol. 47, no. 2 (2006), p. 102-110**Full Text:**false**Reviewed:****Description:**A (k;g)-cage is k-regular graph with girth g and with the least possible number of vertices. In this article we prove that (k;g)-cages are edge-superconnected if g is even. Earlier, Marcote and Balbuena proved that (k;g)-cages are edge-superconnected if g is odd [Networks 43 (2004), 54-59]. Combining our results, we conclude that all (k;g)-cages are edge-superconnected. © 2005 Wiley Periodicals, Inc.**Description:**C1**Description:**2003001830

All (k;g)-cages are k-edge-connected

- Lin, Yuqing, Miller, Mirka, Rodger, Chris

**Authors:**Lin, Yuqing , Miller, Mirka , Rodger, Chris**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227**Full Text:**false**Reviewed:****Description:**A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.**Description:**C1

An application of sum labeling for the access structure in a secret sharing scheme

- Miller, Mirka, Sugeng, Kiki Ariyanti, Slamet, Surjadi

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Slamet, Surjadi**Date:**2005**Type:**Text , Conference paper**Relation:**Paper presented at INACISC Indonesia Cryptology and Information Security Conference, Jakarta, Indonesia : 30th - 31st March, 2005**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001405

An open problem : (4; g)-cages with odd g <= 5 are tightly connected

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

**Authors:**Tang, Jianmin , Balbuena, Camino , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at Thirteenth Computing : The Australasian Theory Symposium, CATS2007, Ballarat, Victoria : January 30th-Febuary 2nd p. 141-144**Full Text:**false**Description:**Interconnection networks form an important area which has received much attention, both in theoretical research and in practice. From theoretical point of view, an interconnection network can be modelled by a graph, where the vertices of the graph represent the nodes of the network and the edges of the graph represent connections between the nodes in the network. Fault tolerance is an important performance feature when designing a network, and the connectivity of the underlying graph is one of the measures of fault tolerance for a network. A graph is connected if there is a path between any two vertices of G. We say that G is t-connected if the deletion of at least t vertices of G is required to disconnect the graph. A graph with minimum degree delta is maximally connected if it is delta-connected. A graph is superconnected if its only minimum disconnecting sets are those induced by the neighbors of a vertex; a graph is said to be tightly superconnected if (i) any minimum disconnecting set is the set of neighbors of a single vertex; and (ii) the deletion of a minimum disconnecting set results in a graph with two components (one of which has only one vertex, another component is a connected graph). A (delta; g) - cage is a delta-regular graph with girth g and with the least possible number of vertices. In this paper we consider the problem of whether or not (4; g)-cages for g >= 5 are tightly superconnected. We present some partial results and the remaining open problems.**Description:**Interconnection networks form an important area which has received much attention, both in theoretical research and in practice. From theoretical point of view, an interconnection network can be modelled by a graph, where the vertices of the graph represent the nodes of the network and the edges of the graph represent connections between the nodes in the network. Fault tolerance is an important performance feature when designing a network, and the connectivity of the underlying graph is one of the measures of fault tolerance for a network. A graph is connected if there is a path between any two vertices of G. We say that G is t-connected if the deletion of at least t vertices of G is required to disconnect the graph. A graph with minimum degree \delta\ is maximally connected if it is \delta\-connected. A graph is superconnected if its only minimum disconnecting sets are those induced by the neighbors of a vertex; a graph is said to be tightly superconnected if (i) any minimum disconnecting set is the set of neighbors of a single vertex; and (ii) the deletion of a minimum disconnecting set results in a graph with two components (one of which has only one vertex, another component is a connected graph). A (\delta\; g) - cage is a \delta\-regular graph with girth g and with the least possible number of vertices. In this paper we consider the problem of whether or not (4; g)-cages for g >= 5 are tightly superconnected. We present some partial results and the remaining open problems.**Description:**2003005018

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.

- 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

Antimagic valuations for the special class of plane graphs

- Baca, Martin, Baskoro, Edy, Miller, Mirka

**Authors:**Baca, Martin , Baskoro, Edy , Miller, Mirka**Date:**2005**Type:**Text , Journal article**Relation:**Lecture Notes in Computer Science Vol. 3350, no. (2005), p. 58-64**Full Text:**false**Reviewed:****Description:**We deal with the problem of labeling the vertices, edges and faces of a special class of plane graphs with 3-sided internal faces 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 the weight of that face. These face weights then form an arithmetic progression with common difference d.**Description:**C1**Description:**2003001410

Calculating the extremal number ex (v ; {C3, C4, ..., Cn})

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

**Authors:**Tang, Jianmin , Lin, Yuqing , Miller, Mirka**Date:**2006**Type:**Text , Journal article**Relation:**Electronic Notes in Discrete Mathematics Vol. 27, no. (2006), p. 101-102**Full Text:**false**Reviewed:****Description:**This paper introduces and analyzes a parallel method of simulated annealing. Borrowing from genetic algorithms, an effective combination of simulated annealing and genetic algorithms, called parallel recombinative simulated annealing, is developed. This new algorithm strives to retain the desirable asymptotic convergence properties of simulated annealing, while adding the populations approach and recombinative power of genetic algorithms. The algorithm iterates a population of solutions rather than a single solution, employing a binary recombination operator as well as a unary neighborhood operator. Proofs of global convergence are given for two variations of the algorithm. Convergence behavior is examined, and empirical distributions are compared to Boltzmann distributions. Parallel recombinative simulated annealing is amenable to straightforward implementation on SIMD, MIMD, or shared-memory machines. The algorithm, implemented on the CM-5, is run repeatedly on two deceptive problems to demonstrate the added implicit parallelism and faster convergence which can result from larger population sizes.**Description:**C1

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

Complete catalogue of graphs of maximum degree 3 and defect at most 4

- Miller, Mirka, Pineda-Villavicencio, Guillermo

**Authors:**Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**Discrete Applied Mathematics Vol. 157, no. 13 (2009), p. 2983-2996**Full Text:****Reviewed:****Description:**We consider graphs of maximum degree 3, diameter D≥2 and at most 4 vertices less than the Moore bound M3,D, that is, (3,D,−)-graphs for ≤4. We prove the non-existence of (3,D,−4)-graphs for D≥5, completing in this way the catalogue of (3,D,−)-graphs with D≥2 and ≤4. Our results also give an improvement to the upper bound on the largest possible number N3,D of vertices in a graph of maximum degree 3 and diameter D, so that N3,D≤M3,D−6 for D≥5. Copyright Elsevier.

**Authors:**Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**Discrete Applied Mathematics Vol. 157, no. 13 (2009), p. 2983-2996**Full Text:****Reviewed:****Description:**We consider graphs of maximum degree 3, diameter D≥2 and at most 4 vertices less than the Moore bound M3,D, that is, (3,D,−)-graphs for ≤4. We prove the non-existence of (3,D,−4)-graphs for D≥5, completing in this way the catalogue of (3,D,−)-graphs with D≥2 and ≤4. Our results also give an improvement to the upper bound on the largest possible number N3,D of vertices in a graph of maximum degree 3 and diameter D, so that N3,D≤M3,D−6 for D≥5. Copyright Elsevier.

Complete characterization of almost moore digraphs of degree three

- Baskoro, Edy, Miller, Mirka, Siran, Jozef, Sutton, Martin

**Authors:**Baskoro, Edy , Miller, Mirka , Siran, Jozef , Sutton, Martin**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 48, no. 2 (2005), p. 112-126**Full Text:**false**Reviewed:****Description:**It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In this paper, we prove that digraphs of degree three and diameter k ≥ 3 which miss the Moore bound by one do not exist. © 2004 Wiley Periodicals, Inc.**Description:**C1**Description:**2003000904

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

- Balbuena, Camino, Barker, Ewan, Lin, Yuqing, Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**Balbuena, Camino , Barker, Ewan , Lin, Yuqing , Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 16 (2006), p. 1817-1829**Full Text:**false**Reviewed:****Description:**Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1, 2, ..., n + e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is { a + 1, a + 2, ..., a + n }, and is b-edge consecutive magic if the set of labels of the edges is { b + 1, b + 2, ..., b + e }. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n - 1)**Description:**C1**Description:**2003001604

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

Cordial labelling of butterfly networks and mesh of trees

- Miller, Mirka, Rajan, Bharati, Rajasingh, Indra, Manuel, Paul

**Authors:**Miller, Mirka , Rajan, Bharati , Rajasingh, Indra , Manuel, Paul**Date:**2006**Type:**Text , Conference paper**Relation:**Paper presented at AWOCA 2006, 17th Australasian Workshop on Combinatorial Algorithms, Uluru, Australia : 13th July, 2006**Full Text:**false**Reviewed:****Description:**E1**Description:**2003001646

Delta-optimum exclusive sum labeling of certain graphs with radius one

- Tuga, Mauritsius, Miller, Mirka

**Authors:**Tuga, Mauritsius , Miller, Mirka**Date:**2005**Type:**Text , Journal article**Relation:**Lecture Notes in Computer Science Vol. 3330, no. (2005), p. 216-225**Full Text:**false**Reviewed:****Description:**A mapping**Description:**C1**Description:**2003001413

Diameter-sufficient conditions for a graph to be super-restricted connected

- Balbuena, Camino, Lin, Yuqing, Miller, Mirka

**Authors:**Balbuena, Camino , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Applied Mathematics Vol. , no. (2007), p.**Full Text:**false**Reviewed:****Description:**A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G - X must have at least two vertices. The restricted connectivity**Description:**C1

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