Signless Laplacian determinations of some graphs with independent edges - Sharafdini, R.; Abdian, A.Z. (Carpathian Mathematical Publications, 2018)
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 GrK_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.