Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2018

Journal or Book Title

Discrete Mathematics

DOI

10.1016/j.disc.2017.10.031

Abstract

Zero forcing and power domination are iterative processes on graphs where an initial set of vertices are observed, and additional vertices become observed based on some rules. In both cases, the goal is to eventually observe the entire graph using the fewest number of initial vertices. The concept of k-power domination was introduced by Chang et al. (2012) as a generalization of power domination and standard graph domination. Independently, k-forcing was defined by Amos et al. (2015) to generalize zero forcing. In this paper, we combine the study of k-forcing and k-power domination, providing a new approach to analyze both processes. We give a relationship between the k-forcing and the k-power domination numbers of a graph that bounds one in terms of the other. We also obtain results using the contraction of subgraphs that allow the parallel computation of k-forcing and k-power dominating sets.

Comments

This is a manuscript of the article Ferrero, Daniela, Leslie Hogben, Franklin HJ Kenter, and Michael Young. "The relationship between k-forcing and k-power domination." Discrete Mathematics (2018). DOI: 10.1016/j.disc.2017.10.031. Posted with permission.

Rights

Works produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted.

Language

en

File Format

application/pdf

Published Version

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