K-Tuple Total Domination in Complementary Prisms. (18th January 2012) - Kazemi Kazemi, Adel P. Adel P.
Abstract : Let k be a positive integer, and let G be a graph with minimum degree at least k . In their study (2010), Henning and Kazemi defined the k -tuple total domination number γ × k, t G of G as the minimum cardinality of a k -tuple total dominating set of G, which is a vertex set such that every vertex of G is adjacent to at least k vertices in it. If G ̅ is the complement of G, the complementary prism G G ̅ of G is the graph formed from the disjoint union of G and G ̅ by adding the edges of a perfect matching between the corresponding vertices of G and G ̅ . In this paper, we extend some of the results of Haynes et al. (2009) for the k -tuple total domination number and also obtain some other new results. Also we find the k -tuple total domination number of the complementary prism of a cycle, a path, or a complete multipartite graph.