On the total k-domination in graphs
Sergio Bermudo, Juan C. Hernández‐Gómez, José María Sigarreta · Discussiones Mathematicae Graph Theory · 2017
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 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 domination parameters of the graph.