The Laplacian energy of conjugacy class graph of some dihedral groups

Abstract

Let G be a dihedral group and Gamma its conjugacy class graph. The Laplacian energy of the graph, LE(Gamma) 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 number of vertices. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups and its eigenvalues are first computed. Then, the Laplacian energy of this graph is determined.