Complementary total domination in graphs

Let D be a minimum total dominating set of G. If V−D contains a total dominating set (TDS) say S of G, then S is called a complementary total dominating set with respect to D. The complementary total domination number γ ct (G) of G is the minimum number of vertices in a complementary total dominating set (CTDS) of G .In this paper, exact values of γ ct (G) for some standard graphs are obtained. Also its relationship with other domination related parameters are investigated