The total domination and total bondage numbers of extended de Bruijn and Kautz digraphs

AbstractIn this paper we consider the total domination number and the total bondage number for digraphs. The total bondage number, defined as the minimum number of edges whose removal enlarges the total domination number, measures to some extent the robustness of a network where a minimum total dominating set is required. We determine the total domination number and total bondage number of the extended de Burijn digraph and the extended Kautz digraph, proposed by Shibata and Gonda in 1995, which generalize the classical de Bruijn digraph and the Kautz digraph