k-Tuple Total Domination in Supergeneralized Petersen Graphs - Kazemi, Adel P.; Pahlavsay, Behnaz (Communications in Mathematics and Applications, 2011)
Total domination number of a graph without isolated vertex is the minimum cardinality of a total dominating set, that is, a set of vertices such that every vertex of the graph is adjacent to at least one vertex of the set. Henning and Kazemi in [4] extended this definition as follows: for any positive integer k, and any graph G with minimum degree-k, a set D of vertices is a k-tuple total dominating set of G if each vertex of G is adjacent to at least k vertices in D. The k-tuple total domination number γ _× k,t(G) of G is the minimum cardinality of a k-tuple total dominating set of G. In this paper, we give some upper bounds for the k-tuple total domination number of the supergeneralized Petersen graphs. Also we calculate the exact amount of this number for some of them.