Trees with a large Laplacian eigenvalue multiplicity

被引：3
|
作者：
Akbari, S. [1 ]
van Dam, E. R. [2 ]
Fakharan, M. H. [1 ]
机构：
[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran
[2] Tilburg Univ, Dept Econometr & OR, Tilburg, Netherlands
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 586卷
基金：
美国国家科学基金会;
关键词：
Laplacian spectrum; Trees; Multiplicities of eigenvalues; ALGEBRAIC CONNECTIVITY;
D O I：
10.1016/j.laa.2019.10.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than 1 are simple and also the multiplicity of Laplacian eigenvalue 1 has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order n that have a multiplicity that is close to the upper bound n-3/2, and emphasize the particular role of the algebraic connectivity. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：262 / 273
页数：12
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