The signless Laplacian spectrum of the (edge) corona of two graphs

Abstract

Let G1, G2 be two graphs. Denote the corona and the edge corona of G1, G2 by G1 ○ G2 and G1 ◇ G2, respectively. In this paper, the signless Laplacian spectrum of G1 ○ G2 and G1 ◇G2 are given in terms of the signless Laplacian spectrum of G1 and G2. As an application of these results, we construct many pairs of nonisomorphic signless Laplacian cospectral graphs.