An Eternal Domination Problem in Grids

Authors

William Klostermeyer, University of North FloridaFollow
Margaret-Ellen MessingerFollow
Alejandro Angeli AyelloFollow

Publication Date

2017

Abstract

A dynamic domination problem in graphs is considered in which an infinite sequence of attacks occur at vertices with mobile guards; the guard at the attacked vertex is required to vacate the vertex by moving to a neighboring vertex with no guard. Other guards are allowed to move at the same time, and before and after each attack, the vertices containing guards must form a dominating set of the graph. The minimum number of guards that can defend the graph against such an arbitrary sequence of attacks is called the m-eviction number of the graph. In this paper, the m-eviction number is determined exactly for small grids with and upper bounds are given for all m ≥ n ≥ 8.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Klostermeyer, William; Messinger, Margaret-Ellen; and Angeli Ayello, Alejandro (2017) "An Eternal Domination Problem in Grids," Theory and Applications of Graphs: Vol. 4: Iss. 1, Article 2.
DOI: 10.20429/tag.2017.040102
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol4/iss1/2