• COMPLEMENTARY EQUIVALENCE DOMINATING SETS IN GRAPHS

Abstract

Let  be a simple finite undirected graph.  A subset S of V(G) is called an equivalence set if every component of the induced sub graph  is complete. A graph G is an equivalence graph if every component of G is complete. A subset S of V(G) is called a complementary equivalence dominating set of G if  is an equivalence set of G and S is a dominating set of G. The minimum cardinality of a c-e-d set of G is denoted by ).  In this paper, several results concerning complementary equivalence domination are derived Also Complementary equivalence irredundance is defined and relationship between the minimum cardinality of a maximal c-e irredundance set of G and  are found. Further Independence c-e saturation parameter is also introduced.