Signless Laplacian determinations of some graphs with independent edges

Karpatsʹkì Matematičnì Publìkacìï

R. Sharafdini¹  A.Z. Abdian² 

[1] Department of Mathematics, Persian Gulf University, Bushehr 7516913817, Iran;Department of the mathematical Science, College of Science, Lorestan University, Lorestan, Khoramabad 41566, Iran;

关键词: spectral characterization;    signless laplacian spectrum;    cospectral graphs;    union of graphs;   

DOI  :  10.15330/cmp.10.1.185-196

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown