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The competition number of a graph with

โœ Scribed by Bo-Jr Li; Gerard J. Chang

Book ID
106407376
Publisher
Springer US
Year
2010
Tongue
English
Weight
349 KB
Volume
23
Category
Article
ISSN
1382-6905

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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

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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