On the global total k-domination number of graphs

A subset D of vertices of a graph G is a global total k-dominating set if D is a total k-dominating set of both G and (G) over bar. The global total k-domination number of G is the minimum cardinality of a global total k-dominating set of G and it is denoted by gamma(g)(kt)(G). In this paper we introduce this concept and we begin the study of its mathematical properties. Specifically, we prove that the complexity of the decision problem associated to the computation of the value gamma(g)(kt) (G) is NP-complete. Moreover, we present tight bounds for this parameter and we obtain relationships between the global total k-domination number of G and the total k-domination numbers of G and (G) over bar, and other parameters of the graph G. (C) 2018 Elsevier B.V. All rights reserved.