Abstract

We introduce the concept of stable index for 0-1 matrices. Let A be a 0-1 square matrix. If Ak is a 0-1 matrix for every positive integer k, then the stable index of A is defined to be infinity; otherwise, the stable index of A is defined to be the smallest positive integer k such that Ak+1 is not a 0-1 matrix. We determine the maximum finite stable index of all 0-1 matrices of order n as well as the matrices attaining the maximum finite stable index.

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