%0 Generic %1 chen2019stable %A Chen, Zhibing %A Huang, Zejun %A Yan, Jingru %D 2019 %K Graph matrix %T The stable index of 0-1 matrices %U http://arxiv.org/abs/1912.03912 %X We introduce the concept of stable index for 0-1 matrices. Let $A$ be a 0-1 square matrix. If $A^k$ 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 $A^k+1$ 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.

@misc{chen2019stable, abstract = {We introduce the concept of stable index for 0-1 matrices. Let $A$ be a 0-1 square matrix. If $A^k$ 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 $A^{k+1}$ 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.}, added-at = {2019-12-11T04:19:36.000+0100}, author = {Chen, Zhibing and Huang, Zejun and Yan, Jingru}, biburl = {https://www.bibsonomy.org/bibtex/29d57b05d5ada05f12680d9536d74ce50/j.c.m.janssen}, description = {The stable index of 0-1 matrices}, interhash = {ad350901824fdbf391eae00b8d39de57}, intrahash = {9d57b05d5ada05f12680d9536d74ce50}, keywords = {Graph matrix}, note = {cite arxiv:1912.03912}, timestamp = {2019-12-11T04:19:36.000+0100}, title = {The stable index of 0-1 matrices}, url = {http://arxiv.org/abs/1912.03912}, year = 2019 }