Complementary total domination in graphs

Abstract

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.

Keywords and phrases:

• Graphs
• domination
• total domination
• complementary total domination