COMPLEMENTARY FAIR DOMINATION IN GRAPHS

Abstract

In a simple, finite undirected graph G, a dominating set D is a subset of the vertex set V(G) whose closed neighbourhood is V(G). Many types of domination have been studied. The studies are based either on the nature of domination or the type of dominating set or the type of the complement of the dominating set. Interaction between dominating set and its complement is also considered. Fair domination is the domination where every vertex in the complement of a dominating set has equal number of neighbours in the dominating set. In this paper, a dominating set whose vertices have equal number of neighbours in the complement is the subject of study. The parameter γ_cof (G) is introduced and studied.