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http://dx.doi.org/10.4134/BKMS.2013.50.6.2001

THE COMPETITION INDEX OF A NEARLY REDUCIBLE BOOLEAN MATRIX  

Cho, Han Hyuk (Department of Mathematics Education Seoul National University)
Kim, Hwa Kyung (Department of Mathematics Education Sangmyung University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 2001-2011 More about this Journal
Abstract
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.
Keywords
competition graph; m-step competition graph; competition index; competition period; scrambling index;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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