On the kth Laplacian eigenvalues of trees with perfect matchings

被引:6
作者
Li, Jianxi [1 ]
Shiu, Wai Chee [1 ]
Chang, An [2 ]
机构
[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
[2] Fuzhou Univ, Software Coll, Ctr Discrete Math, Fuzhou 350002, Fujian, Peoples R China
基金
中国国家自然科学基金;
关键词
Tree; Laplacian eigenvalue; Perfect matchings; Bound;
D O I
10.1016/j.laa.2009.10.015
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let T-n(+) be the set of all trees of order n with perfect matchings. In this paper, we prove that for any tree T is an element of T-n(+), its kth largest Laplacian eigenvalue mu(k)(T) satisfies mu(k)(T) = 2 when n = 2k, and mu(k)(T) <= [n/2k]+2+ root([n/2k](2)+4/2 when n not equal 2k. Moreover, this upper bound is sharp when n = 0(mod 2k). (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:1036 / 1041
页数:6
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