Operator power graph of a group

Let (G, ∗) be a group with binary operation ‘∗′. The Operator Power graph ΓOP (G) of G is a graph with V (ΓOP (G)) = G and two distinct vertices x and y are adjacent in ΓOP (G) if and only if either x = (x∗y)n or y = (x ∗ y)m, where n,m are positive integers. In this paper, we want to explore how the group theoretical properties of G can effect on the graph theoretical properties of ΓOP (G). Some characterizations for fundamental properties of ΓOP (G) have also been obtained. Mathematics Subject Classification: 05C25, 20A05