Abstract
Let G1,G2 be two simple connected graphs. Denote the corona and the edge corona of G1,G2 by G1∘G2 and G1♢G2, respectively. In this paper, we first introduce a new invariant, the M-coronal of a graph matrix M, where the matrix M is associated with a graph in a prescribed way. Then it is used to compute the signless Laplacian spectrum of G1∘G2 and G1♢G2 in terms of the signless Laplacian spectrum of G1 and G2. In addition, the spectrum of G1♢G2 are also given in terms of the spectrum of G1 and G2. Finally, as an application of these results, we construct many pairs of nonisomorphic signless Laplacian cospectral graphs.
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