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On the Totalk-Domination in Graphs

Sergio Bermudo;  Juan C. Hernández-Gómez;  José M. Sigarreta — 2018

Discussiones Mathematicae Graph Theory

Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination...

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