On the monotonicity of the number of positive entries in nonnegative five-element matrix powers

Rodriguez Galvan, Matthew; Ponomarenko, Vadim; Salvadore Sabio, John

doi:10.2140/involve.2021.14.703

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

This article is available for purchase or by subscription. See below.

On the monotonicity of the number of positive entries in nonnegative five-element matrix powers

Matthew Rodriguez Galvan, Vadim Ponomarenko and John Salvadore Sabio

Vol. 14 (2021), No. 4, 703–721

DOI: 10.2140/involve.2021.14.703

Abstract

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

PDF Access Denied

We have not been able to recognize your IP address 18.222.115.120 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords

nonnegative matrix, power, monotonicity, directed graph, adjacency matrix

Mathematical Subject Classification

Primary: 05C20, 15B34, 15B48

Milestones

Received: 12 March 2021

Revised: 10 April 2021

Accepted: 28 April 2021

Published: 23 October 2021

Communicated by Ronald Gould

Authors

Matthew Rodriguez Galvan
Department of Mathematics and Statistics San Diego State University San Diego, CA United States

Vadim Ponomarenko
Department of Mathematics and Statistics San Diego State University San Diego, CA United States

John Salvadore Sabio
Department of Computer Science San Diego State University San Diego, CA United States

Vol. 14, No. 4, 2021