descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2014 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae Graph Theory, volume 35, page 283 (issn: 1234-3099, eissn: 2083-5892,

Authors: Christina M. Mynhardt; William F. Klostermeyer;

doi: 10.7151/dmgt.1799 , 10.48550/arxiv.1407.5235

arXiv: http://arxiv.org/abs/1407.5235

Domination, eternal domination and clique covering

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Abstract

Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique covering numbers of graph are explored in this paper. Among other results, we characterize bipartite and triangle-free graphs with domination and eternal domination numbers equal to two, trees with equal m-eternal domination and clique covering numbers, and two classes of graphs with equal domination, eternal domination and clique covering numbers.

16 pages, 3 figures

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Keywords

independent set, 05C69, clique cover, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, dominating set, Combinatorics (math.CO), eternal dominating set, Mathematics

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