The star matching number and (signless) Laplacian eigenvalues
HE Chang-xiang1, LIU Shi-qiong2
1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2. Affiliated Experimental School of Donghua University, Shanghai 201600, China
Abstract Let $G$ be a simple graph, and $s\leqslant3$ be an integer. In this paper, if $G$ is a connected graph with order $n$ and $K_{1,s}$-matching number $m(G)$, such that $n>(s+1)m(G)$, then the $m(G)$-th largest Laplacian eigenvalue $\mu_{m(G)}>s+1$. And this result also holds for signless spectrum. As an application, some $Q$-eigenvalue conditions which can determine the Hamiltonicity of a graph are listed.
HE Chang-xiang, LIU Shi-qiong. The star matching number and (signless) Laplacian eigenvalues. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 333-339.
