Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

6-2020

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

36

Issue

36

First Page

318

Last Page

333

DOI

10.13001/ela.2020.5127

Abstract

Zero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. Probabilistic zero forcing yields a discrete dynamical system governed by a Markov chain. Since in a connected graph any one vertex can eventually color the entire graph blue using probabilistic zero forcing, the expected time to do this is studied. Given a Markov transition matrix for a probabilistic zero forcing process, an exact formula is established for expected propagation time. Markov chains are applied to determine bounds on expected propagation time for various families of graphs.

Comments

This article is published as Chan, Yu, Emelie Curl, Jesse Geneson, Leslie Hogben, Kevin Liu, Issac Odegard, and Michael Ross. "Using Markov Chains to Determine Expected Propagation Time for Probabilistic Zero Forcing." The Electronic Journal of Linear Algebra 36, no. 36 (2020): 318-333. DOI: 10.13001/ela.2020.5127. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

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