δ-Complement of a Graph

Let G(V,X) be a finite and simple graph of order n size m. The complement G, denoted by G¯, is the obtained removing lines G adding that are not in G. A self-complementary if only it isomorphic to its complement. In this paper, we define δ-complement δ′-complement as follows. For any two points u v with degu=degv remove between add which thus called degu≠degv δ(δ′)-self-complementary G≅Gδ(G≅Gδ′). δ(δ′)-co-self-complementary Gδ≅G¯(Gδ′≅G¯). This paper presents different properties δ given graph.