Connected minimum secure-dominating sets in grids

Johnathan Barnett; Adam Blumenthal; Peter Johnson; Cadavious Jones; Ryan Matzke; Egbert Mujuni

doi:10.1016/j.akcej.2017.03.003

AKCE International Journal of Graphs and Combinatorics (Dec 2017)

Connected minimum secure-dominating sets in grids

Johnathan Barnett,
Adam Blumenthal,
Peter Johnson,
Cadavious Jones,
Ryan Matzke,
Egbert Mujuni

Affiliations

Johnathan Barnett: Department of Mathematics and Statistics, Auburn University
Adam Blumenthal: Department of Mathematics and Statistics, Auburn University
Peter Johnson: Department of Mathematics and Statistics, Auburn University
Cadavious Jones: Department of Mathematics and Computer Science, Alabama State University
Ryan Matzke: Department of Mathematics and Computer Science, Gettysburg College
Egbert Mujuni: Department of Mathematics, University of

DOI: https://doi.org/10.1016/j.akcej.2017.03.003
Journal volume & issue: Vol. 14, no. 3
pp. 216 – 223

Abstract

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For any (finite simple) graph the secure domination number of satisfies . Here we find a secure-dominating set in such that in all cases when is a grid, and in the majority of cases when is a cylindrical or toroidal grid. In all such cases, satisfies the additional requirement that is connected. We make note that the concept of secure-dominating sets considered in this paper is quite different from the other secure domination currently of interest.

Published in AKCE International Journal of Graphs and Combinatorics

ISSN: 0972-8600 (Print); 2543-3474 (Online)
Publisher: Taylor & Francis Group
Country of publisher: United States
LCC subjects: Science: Mathematics
Website: https://www.tandfonline.com/journals/uakc

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