ON SELF COMPLEMENTARITY OF THE INDUCED COMPLEMENT OF A GRAPH

Let G = (V,E) be a graph and S ⊆V. The induced complement of the graph G with respect to the set S, denoted by GS, is the graph obtained from the graph G by removing the edges of ⟨S⟩ of G and adding the edges which are not in ⟨S⟩ of G. Given a set S ⊆V, the graph G is said to be S-induced self complementary if GS ∼= G. The graph G is said to be S-induced co-complementary if GS ∼= G. This paper presents the study of the different properties of the S-i.s.c. and S-i.c.c. graphs.