Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

2016

Journal or Book Title

Discrete Applied Mathematics

Volume

213

First Page

114

Last Page

129

DOI

10.1016/j.dam.2016.05.004

Abstract

An r-fold analogue of the positive semidefinite zero forcing process that is carried out on the r-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number. Properties of the graph blowup when colored with a fractional positive semidefinite forcing set are examined and used to define a three-color forcing game that directly computes the fractional positive semidefinite forcing number of a graph. We develop a fractional parameter based on the standard zero forcing process and it is shown that this parameter is exactly the skew zero forcing number with a three-color approach. This approach and an algorithm are used to characterize graphs whose skew zero forcing number equals zero.

Comments

This is a manuscript of an article from Discrete Applied Mathematics 213 (2016): 114, doi:10.1016/j.dam.2016.05.004. Posted with permission.

Rights

This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier B.V.

Language

en

File Format

application/pdf

Published Version

Share

COinS