Equitable domination of inflated graph of complement

Abstract

Let G be a graph. A subset U of V is called an equitable dominating set of a graph G if for every member a of V-U, there exists a vertex b of U such that ab ∈ E(G) and |d (a) − d (b)| ≤ 1, where d(a) is the degree of a and d(b) is the degree of b in G. The equitable domination number of a graph G is denoted by γ e (G), which is the minimum cardinality of the set U. The inflation graph Gl is obtained from a graph G by modifying every vertex a of degree d(a) by a clique Kd(a). In this paper we study the equitable domination number of inflated graph of complement of some graphs and also study an upper bound of equitable domination number of inflated graph Gl of complement of any graph G.