On the total k-domination in graphs

Sergio Bermudo, Juan Carlos Hernández-Gómez, Jośe 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 γ kt (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
more » ... diameter, and other domination parameters of the graph.
doi:10.7151/dmgt.2016 fatcat:rtzvwaxrnne73ldocdqcib7n7q