The Laplacian energy of conjugacy class graph of some finite groups

Abstract

Let G be a dihedral group and ΓdG its conjugacy class graph. The Laplacian energy of the graph, LE(ΓdG) is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.