Generalized competition index of a primitive digraph |
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Authors: | Hwa Kyung Kim |
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Affiliation: | Department of Mathematics Education, Sangmyung University, Seoul 110-743, South Korea |
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Abstract: | For positive integers k and m, and a digraph D, the k-step m-competition graph of D has the same set of vertices as D and an edge between vertices x and y if and only if there are distinct m vertices v1,v2,…,vm in D such that there are directed walks of length k from x to vi and from y to vi for 1?i?m. In this paper, we present the definition of m-competition index for a primitive digraph. The m-competition index of a primitive digraph D is the smallest positive integer k such that is a complete graph. We study m-competition indices of primitive digraphs and provide an upper bound for the m-competition index of a primitive digraph. |
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Keywords: | 05C50 15A48 05C20 |
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