Domination, eternal domination and clique covering
Copyright policy )Domination, eternal domination and clique covering
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
- University of North Florida United States
- Department of Mathematics and Statistics University of Victoria Canada
- University of Victoria Canada
dominating set, independent set, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), 05C69, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), QA1-939, clique cover, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), eternal dominating set, Mathematics
dominating set, independent set, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), 05C69, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), QA1-939, clique cover, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), eternal dominating set, Mathematics
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