#### Vol. 14, No. 4, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
On the monotonicity of the number of positive entries in nonnegative five-element matrix powers

Vol. 14 (2021), No. 4, 703–721
##### Abstract

Let $A$ be an $m×m$ square matrix with nonnegative entries and let $F\left(A\right)$ denote the number of positive entries in $A$. We consider the adjacency matrix $A$ with a corresponding digraph with $m$ vertices. $F\left(A\right)$ corresponds to the number of directed edges in the corresponding digraph. We consider conditions on $A$ to make the sequence ${\left\{F\left({A}^{n}\right)\right\}}_{n=1}^{\infty }$ monotonic. Monotonicity is known for $F\left(A\right)\le 4$ (except for three nonmonotonic cases) and $F\left(A\right)\ge {m}^{2}-2m+2$; we extend this to $F\left(A\right)=5$.

We have not been able to recognize your IP address 3.236.241.39 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

##### Keywords
nonnegative matrix, power, monotonicity, directed graph, adjacency matrix
##### Mathematical Subject Classification
Primary: 05C20, 15B34, 15B48