The Laplacian Energy of Conjugacy Class Graph of Dihedral Groups
The energy of a graph is defined as the sum of the absolute values of its eigenvalues. These eigenvalues are obtained from the incidence matrix of the graph. The Laplacian energy of a graph is defined as the sum of the absolute deviations (i.e. distance from the mean) of the eigenvalues of its Laplacian matrix. Let be the dihedral group and its conjugacy class graph. In this research, the generalized formula for the Laplacian energy of the conjugacy class graph of dihedral groups are obtained. In this presentation, the Laplacian matrices of the conjugacy class graph of dihedral groups with the eigenvalues are first computed. Then, the Laplacian energy of the graph is determined.