A subset D of V is called an equitable dominating set if for every v ∈ V — D there exists a vertex u ∈ D such that uv ∈ E(G) and |d(u) — d(v)| ≤ 1,where d(u) denotes the degree of vertex u and d(v) denotes the degree of vertex v. The minimum cardinality of such a dominating set is denoted by γe and is called the equitable domination number of G. Degree Equitable domination on Graphs were introduced in [10].This Paper aims at the study of a new concept called equitable graph ofa graph introduced by Prof. E. Sampathkumar. In this paper we show that there is relation between γ(Ge) and γe(G). Further results on the new parameter γ(Ge) are discussed.