THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE

- Journal title : Journal of the Korean Mathematical Society
- Volume 48, Issue 4, 2011, pp.691-702
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2011.48.4.691

Title & Authors

THE COMPETITION NUMBERS OF HAMMING GRAPHS WITH DIAMETER AT MOST THREE

Park, Bo-Ram; Sano, Yoshio;

Park, Bo-Ram; Sano, Yoshio;

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;

Language

English

Cited by

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