Your selections:

Show More

Show Less

HSAGA and its application for the construction of near-Moore digraphs

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

**Authors:**Tang, Jianmin , Miller, Mirka , Lin, Yuqing**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Discrete Algorithms Vol. 6, no. 1 (2008), p. 73-84**Full Text:**false**Reviewed:****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 given diameter k. It is known that simulated annealing and genetic algorithm are effective techniques to identify global optimal solutions. This paper describes our attempt to build a Hybrid Simulated Annealing and Genetic Algorithm (HSAGA) that can be used to construct large digraphs. We present our new results obtained by HSAGA, as well as several related open problems. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

On the connectivity of (k, g)-cages of even girth

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

**Authors:**Lin, Yuqing , Balbuena, Camino , Marcote, Xavier , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 15 (2008), p. 3249-3256**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 give a brief overview of the current results on the connectivity of (k,g)-cages and we improve the current known best lower bound on the vertex connectivity of (k,g)-cages for g even. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

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

- 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

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

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

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka , Youssef, Maged**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1232-1244**Full Text:**false**Reviewed:****Description:**For a graph G = (V, E), a bijection g from V(G) boolean OR E(G) into {1, 2,..., vertical bar V(G)vertical bar + vertical bar E(G)vertical bar} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy E E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if g(V(G)) = {1, 2,..., vertical bar V(G)vertical bar}. We study super (a, d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs. (c) 2006 Elsevier B.V. All rights reserved.**Description:**2003004910

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

- 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

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

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

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

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

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

On d-antimagic labelings of prisms

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

**Authors:**Lin, Yuqing , Slamin, , Baca, Martin , Miller, Mirka**Date:**2004**Type:**Text , Journal article**Relation:**Ars Combinatoria: A Canadian Journal of Combinatorics Vol. 72, no. (2004), p. 65-76**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000907

- «
- ‹
- 1
- ›
- »

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