A survey on the automorphism group of commuting graph and power graph

Let G be a finite group and X be a union of its conjugacy classes. Define C(G;X) to be the graph with vertex set X and x;y ∈ X (x ≠ y) joined by an edge whenever they commute. In the case that X = G, this graph is denoted by D(G). Th e power graph P(G) of a group G is the graph whose vertex set is the group elements and two elements are adjacent if one is a power of the other. In this paper we present a survey of results on automorphism group of commuting graph and power graph.