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The competition numbers of ternary Hamming graphs

โœ Scribed by Boram Park; Yoshio Sano

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
243 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

It is known to be a hard problem to compute the competition number k(G) of a graph G in general. Park and Sano (in press) [16] gave the exact values of the competition numbers of Hamming graphs H(n, q) if 1 โ‰ค n โ‰ค 3 or 1 โ‰ค q โ‰ค 2. In this paper, we give an explicit formula for the competition numbers of ternary Hamming graphs.

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If D is an acyclic digraph, its competition graph is an undirected graph with the same vertex set and an edge between vertices x and y if there is a vertex a so that (x, a) and (y, a) are both arcs of D. If G is any graph, G together with sufficiently many isolated vertices is a competition graph, a