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A bound on the generalized competition index of a primitive matrix using Boolean rank
Authors:Hwa Kyung Kim
Institution:Dept. of Mathematics Education, Sangmyung University, Seoul 110-743, South Korea
Abstract:For a positive integer m where 1?m?n, the m-competition index (generalized competition index) of a primitive digraph is the smallest positive integer k such that for every pair of vertices x and y, there exist m distinct vertices v1,v2,…,vm such that there are directed walks of length k from x to vi and from y to vi for 1?i?m. The m-competition index is a generalization of the scrambling index and the exponent of a primitive digraph. In this study, we determine an upper bound on the m-competition index of a primitive digraph using Boolean rank and give examples of primitive Boolean matrices that attain the bound.
Keywords:05C50  15A48  05C20
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