• OPERATOR INTERSECTION GRAPH OF A GROUP

Abstract

Let (G, ∗) be a group with binary operation ‘∗′. The Operator Intersection graph Γ_OI(G) of G is a graph with V (Γ_OI(G)) = G – e and two distinct vertices x and y are adjacent in Γ_OI(G) if and only if <x∗y>⊆<x>∩ < y >. In this paper, we want to explore how the group theoretical properties of G can effect on the graph theoretical properties of Γ_OI(G). Some characterizations for fundamental properties of Γ_OI(G) have also been obtained. Finally, we characterize certain classes of Operator Intersection Graph corresponding to finite abelian groups.