Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.09.08
  • Published : 2013.11.30
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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.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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