Signless Laplacian determinations of some graphs with independent edges

Keywords: spectral characterization, signless Laplacian spectrum, cospectral graphs, union of graphs
Published online: 2018-07-03

Abstract


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 $G\sqcup rK_2$ 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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How to Cite
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Sharafdini R., Abdian A. Signless Laplacian Determinations of Some Graphs With Independent Edges. Carpathian Math. Publ. 2018, 10 (1), 185-196.