The energy and spectrum of non commuting graph

Abstract

Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph {\Gamma}(G) of G is a graph with vertex set is non central elements of G and two vertices x, y are adjacent if and only if they are commute. In this paper we calculate the energy, Laplacian energy and spectrum of non-commuting graph of dihedral group D2n. Also we will obtain the energy of non-commuting graph of D2n \times D2n and G \times H, where G is a non-abelian finite group and H is an abelian finite group