S. Bermudo, J.C. Hernández-Gómez, J.M. Sigarreta
On the total k-domination in graphs
Discussiones Mathematicae Graph Theory
Received 21.04.2016, Revised 21.12.2016, Accepted 21.12.2016, doi: 10.7151/dmgt.2016
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 parameters of the graph.
k-domination, total k-domination, k-tuple domination, k-tuple total domination