Remarks On Commuting Graph of a Finite Group

The commuting graph Δ(G) of a group G is the graph whose vertex set is the group and two distinct elements x and y being adjacent if and only if xy=yx. In this paper the automorphism group of this graph is investigated. We observe that Aut(Δ(G)) is a non-abelian group such that its order is not prime power and square-free.