A bound on the generalized competition index of a primitive matrix using Boolean rank |
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Authors: | Hwa Kyung Kim |
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Institution: | Dept. of Mathematics Education, Sangmyung University, Seoul 110-743, South Korea |
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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. |
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Keywords: | 05C50 15A48 05C20 |
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