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Article
The relationship between k-forcing and k-power domination
Discrete Mathematics
  • Daniela Ferrero, Texas State University
  • Leslie Hogben, Iowa State University
  • Franklin H.J. Kenter, United States Naval Academy
  • Michael Young, Iowa State University
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
1-1-2018
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
Citation Information
Daniela Ferrero, Leslie Hogben, Franklin H.J. Kenter and Michael Young. "The relationship between k-forcing and k-power domination" Discrete Mathematics (2018)
Available at: http://0-works.bepress.com.library.simmons.edu/leslie-hogben/85/