• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.637-646
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• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.