The kirchhoff index and Laplacian spectrum of coronae

Abstract

Let G1, G2 be two simple graphs. Denote the corona and the edge corona of G1, G2 by G1 o G2 and G1 o G2, respectively. This paper gives the Laplacian polynomials of G1 o G2 and G1 o G2 in terms of the Laplacian polynomials of G1 and G2. Using these results, we obtain the Laplacian spectra of G1 o G2 and G1 o G2 in terms of the Laplacian spectra of G1 and G2. As some applications of these results, we construct many pairs of nonisomorphic Laplacian cospectral graphs and compute the Kirchhoff indices of G1 o G2 and G1 o G2. © 2015 Utilitas Mathematics.