Proof of a problem on Laplacian eigenvalues of trees

被引：1

作者：

Yuan, Xiying ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 503卷

关键词：

Tree; Perfect matching; k-th Laplacian eigenvalue;

D O I：

10.1016/j.laa.2016.03.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Denote by mu(k)(L(T)) the k-th Laplacian eigenvalue of a tree T. Let tau(k) (2t) be the set of all trees of order 2tk with perfect matchings. In this note, the trees T in tau(k) (2t) with mu(k) (L(T)) = t+2-I-root t(2)+4/2 are characterized, which solves Problem of J.X. Li, W.C. Shiu and A. Chang in [3] completely. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：180 / 189

页数：10

共 7 条

[1] Cvetkovi DM., 1980, Spectra of Graphs: Theory and Applications
[2] Cvetkovic D., 2010, An Introduction to the Theory of Graph Spectra
[3] GUO J, 2001, LINEAR ALGEBRA ITS A, V325, P71
[4] On the Laplacian spectral radius of a tree
Guo, JM
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 368 : 379 - 385
[5] On the kth Laplacian eigenvalues of trees with perfect matchings
Li, Jianxi
Shiu, Wai Chee
Chang, An
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (04) : 1036 - 1041
[6] BOUNDS ON THE KTH EIGENVALUES OF TREES AND FORESTS
SHAO, JY
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 149 : 19 - 34
[7] Note on the kth Laplacian eigenvalues of trees with perfect matchings
Yuan, Xi-Ying
Guo, Ji-Ming
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 483 : 115 - 127

← 1 →