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http://dx.doi.org/10.4134/JKMS.2011.48.4.691

THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE  

Park, Bo-Ram (Department of Mathematics Education Seoul National University)
Sano, Yoshio (National Institute of Informatics Tokyo)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 691-702 More about this Journal
Abstract
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.
Keywords
competition graph; competition number; edge clique cover; Hamming graph;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
연도 인용수 순위
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