Domination and total domination in complementary prisms

Let G be a graph and be the complement of G. The complementary prism of G is the graph formed from the disjoint union of G and by adding the edges of a perfect matching between the corresponding vertices of G and . For example, if G is a 5-cycle, then is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, and , where γ(G) and γ _t (G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds. Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.