The competition index of a nearly reducible Boolean matrix
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Cho and Kim [4] have introduced the concept of the compe- tition index of a digraph. Similarly, the competition index of an n × n Boolean matrix A is the smallest positive integer q such that Aq+i(AT )q+i = Aq+r+i(AT )q+r+i for some positive integer r and every nonnegative integer i, where AT 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 com- petition index of a nearly reducible Boolean matrix.
Abstract
Cho and Kim [4] have introduced the concept of the compe- tition index of a digraph. Similarly, the competition index of an n × n Boolean matrix A is the smallest positive integer q such that Aq+i(AT )q+i = Aq+r+i(AT )q+r+i for some positive integer r and every nonnegative integer i, where AT 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 com- petition index of a nearly reducible Boolean matrix.
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