Connected minimum secure-dominating sets in grids

Connected minimum secure-dominating sets in grids

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...

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Bibliographic Details
Main Authors: Johnathan Barnett, Adam Blumenthal, Peter Johnson, Cadavious Jones, Ryan Matzke, Egbert Mujuni
Format: Article
Language:English
Published: Taylor & Francis Group 2017-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
security in graphs
dominating sets
hub sets
Online Access:http://dx.doi.org/10.1016/j.akcej.2017.03.003
Description
Summary: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.
ISSN:0972-8600

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