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Abstract
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Let G be a simple undirected graph. Then the signless Laplacian matrix of G is defined as
D G A G in which D G and A G denote the degree matrix and the adjacency matrix of G, respectively.
The graph G is said to be determined by its signless Laplacian spectrum (DQS, for short), if any
graph having the same signless Laplacian spectrum as G is isomorphic to G. We show that G t rK 2
is determined by its signless Laplacian spectra under certain conditions, where r and K 2 denote a
natural number and the complete graph on two vertices, respectively. Applying these results, some
DQS graphs with independent edges are obtained.
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