Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2-15-2019

Journal or Book Title

Discrete Applied Mathematics

Volume

254

First Page

33

Last Page

46

DOI

10.1016/j.dam.2018.06.017

Abstract

Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size of the initial blue vertex set and the number of the time steps needed to color the graph. We study throttling for positive semidefinite zero forcing. We establish a tight lower bound on the positive semidefinite throttling number as a function of the order, maximum degree, and positive semidefinite zero forcing number of the graph, and determine the positive semidefinite throttling numbers of paths, cycles, and full binary trees. We characterize the graphs that have extreme positive semidefinite throttling numbers.

Comments

This is a manuscript of an article published as Carlson, Joshua, Leslie Hogben, Jürgen Kritschgau, Kate Lorenzen, Michael S. Ross, Seth Selken, and Vicente Valle Martinez. "Throttling positive semidefinite zero forcing propagation time on graphs." Discrete Applied Mathematics 254 (2019): 33-46. DOI: 10.1016/j.dam.2018.06.017. Posted with permission.

Copyright Owner

Elsevier B.V.

Language

en

File Format

application/pdf

Available for download on Tuesday, July 07, 2020

Published Version

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