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

页码：262 / 273

页数：12

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