Square graphs of finite groups

An undirected graph called Square graph Γ(G) of a finite group G is introduced and defined as an undirected simple graph whose vertex set is G and two distinct vertices a and b are adjacent if and only if a2 = b or b2 = a. In this paper, for a finite group G, the number of edges of Γ(G) is computed. An upper bound to the clique number of Γ(G) and upper bound to the maximum degree of square graphs of finite cyclic groups are obtained.