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图的无符号拉普拉斯和距离无符号拉普拉斯特征值
引用本文:田凤雷,李晓明,柔建玲.图的无符号拉普拉斯和距离无符号拉普拉斯特征值[J].数学研究及应用,2014,34(6):647-654.
作者姓名:田凤雷  李晓明  柔建玲
作者单位:中国矿业大学理学院, 江苏 徐州 221116;中国矿业大学理学院, 江苏 徐州 221116;中国矿业大学理学院, 江苏 徐州 221116
基金项目:国家自然科学基金 (Grant No.11171343).
摘    要:Let G be a simple graph. We first show that ■, where δiand di denote the i-th signless Laplacian eigenvalue and the i-th degree of vertex in G, respectively.Suppose G is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from G. In addition, for the distance signless Laplacian spectral radius ρQ(G), we determine the extremal graphs with the minimum ρQ(G) among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively.

关 键 词:无符号拉普拉斯    距离无符号拉普拉斯    谱半径    特征值.
收稿时间:2014/2/17 0:00:00
修稿时间:2014/6/30 0:00:00

A Note on the Signless Laplacian and Distance Signless Laplacian Eigenvalues of Graphs
Fenglei TIAN,Xiaoming LI and Jianling ROU.A Note on the Signless Laplacian and Distance Signless Laplacian Eigenvalues of Graphs[J].Journal of Mathematical Research with Applications,2014,34(6):647-654.
Authors:Fenglei TIAN  Xiaoming LI and Jianling ROU
Institution:Department of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China;Department of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China;Department of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China
Abstract:Let $G$ be a simple graph. We first show that $ \delta_i\geq d_i-\sqrt{\lfloor \frac{i}{2} \rfloor \lceil \frac{i}{2} \rceil}$, where $\delta_i$ and $d_i$ denote the $i$-th signless Laplacian eigenvalue and the $i$-th degree of vertex in $G$, respectively. Suppose $G$ is a simple and connected graph, then some inequalities on the distance signless Laplacian eigenvalues are obtained by deleting some vertices and some edges from $G$. In addition, for the distance signless Laplacian spectral radius $\rho_{\mathcal{Q}}(G)$, we determine the extremal graphs with the minimum $\rho_{\mathcal{Q}}(G)$ among the trees with given diameter, the unicyclic and bicyclic graphs with given girth, respectively.
Keywords:signless Laplacian  distance signless Laplacian  spectral radius  eigenvalues  
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