Your selections:

17Baca, Martin
15Lin, Yuqing
14Sugeng, Kiki Ariyanti
13Ryan, Joe
9Pineda-Villavicencio, Guillermo
7Balbuena, Camino
6Baskoro, Edy
5Slamin,
4Dafik
4Nguyen, Minh Hoang
3Cholily, Yus Mochamad
3Gimbert, Joan
3Marcote, Xavier
3Simanjuntak, Rinovia
3Tuga, Mauritsius
2Barker, Ewan
2Delorme, Charles
2Feria-Purón, Ramiro
2Jendrol, Stanislav

Show More

Show Less

460101 Pure Mathematics
14Graph theory
80802 Computation Theory and Mathematics
8Antimagic labeling
7Degree/diameter problem
7Moore bound
50103 Numerical and Computational Mathematics
5Connectivity
5Numerical methods
4Number theory
4Set theory
4Theorem proving
308 Information and Computing Sciences
3Bipartite Moore graphs
3Defect
3Diameter
3Graph labeling
3Integer programming
3Moore graphs
3Problem solving

Show More

Show Less

Format Type

Structure of repeat cycles in almost Moore digraphs with selfrepeats and diameter 3

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

**Authors:**Miller, Mirka , Baskoro, Edy , Cholily, Yus Mochamad**Date:**2006**Type:**Text , Journal article**Relation:**Bulletin of the Institute of Combinatorics and its Applications Vol. 46, no. (2006), p. 99-109**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001829

Sum graph based access structure in a secret sharing scheme

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

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

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

Survey of edge antimagic labelings of graphs

- Miller, Mirka, Baca, Martin, Baskoro, Edy, Ryan, Joe, Simanjuntak, Rinovia, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Baca, Martin , Baskoro, Edy , Ryan, Joe , Simanjuntak, Rinovia , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Indonesian Mathematical Society, MIHMI Vol. 12, no. 1 (2006), p. 113-130**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001600

Two new families of large compound graphs

- Marti, J. Gomez, Miller, Mirka

**Authors:**Marti, J. Gomez , Miller, Mirka**Date:**2006**Type:**Text , Journal article**Relation:**Networks Vol. 47, no. 3 (2006), p. 140-146**Full Text:**false**Reviewed:****Description:**A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree A and diameter D. Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known (Δ, D)-graphs. © 2006 Wiley Periodicals, Inc.**Description:**C1**Description:**2003001599

Vertex-magic total labeling of generalized Petersen graphs and convex polytopes

- Miller, Mirka, Baca, Martin, MacDougall, James

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

(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

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

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

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

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

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

Improved lower bound for the vertex connectivity of (delta;g)-cages

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

**Authors:**Lin, Yuqing , Miller, Mirka , Balbuena, Camino**Date:**2005**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 299, no. 1-3 (Aug 2005), p. 162-171**Full Text:**false**Reviewed:****Description:**A (delta, g)-cage is a delta-regular graph with girth g and with the least possible number of vertices. We prove that all (delta, g)-cages are r-connected with r >= root(delta + 1) for g >= 7 odd. This result supports the conjecture of Fu, Huang and Rodger that all (delta; g)-cages are delta-connected. (c) 2005 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003001397

Languages recognized by two-sided automata of graphs

- Miller, Mirka, Kelarev, Andrei, Sokratova, Olga

**Authors:**Miller, Mirka , Kelarev, Andrei , Sokratova, Olga**Date:**2005**Type:**Text , Journal article**Relation:**Proceedings of the Estonian Academy of Sciences, Physics Mathematic Vol. 51, no. 1 (2005), p. 46-54**Full Text:**false**Reviewed:****Description:**We introduce two-sided automata defined by directed graphs and describe all languages recognized by these automata.**Description:**C1**Description:**2003001399

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

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

Relationship between adjacency matrices and super (a,d)-edge-antimagic total labeling of graphs

- Miller, Mirka, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 71-82**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001403

Super (a,d)-vertex-antimagic total labelings

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

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Lin, Yuqing , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 91-102**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001401

Are you sure you would like to clear your session, including search history and login status?