The set of stable indices of 0-1 matrices with a given order

Abstract

The stable index of a 0-1 matrix $A$ is defined to be the smallest integer $k$ such that $A^{k+1}$ is not a 0-1 matrix if such an integer exists; otherwise the stable index of $A$ is defined to be infinity. We characterize the set of stable indices of 0-1 matrices with a given order.