Complementary Nil Eccentric Domination Number of a Graph

Abstract

A subset D of the vertex set V (G) of a graph G is said to be a dominating set if every vertex not in D is adjacent to atleast one vertex in D. A dominating set D is said to be an eccentric dominating set if for every v ∈ V − D, there exists atleast one eccentric point of v in D. An eccentric dominating set D of G is a complementary nil eccentric dominating set if the induced subgraph < V − D > is not an eccentric dominating set for G. The minimum of the cardinalities of the complementary nil eccentric dominating sets of G is called the complementary nil eccentric domination number γ cned (G) of G. In this paper, bounds for γ cned (G), its exact value for some particular classes of graphs and some results on complementary nil eccentric domination number are obtained.