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
相关论文
共 50 条
  • [1] A relation between multiplicity of 1 as a Laplacian eigenvalue and induced matching numbers in trees
    Wang, Zhiwen
    Chen, Qian-Qian
    Guo, Ji-Ming
    Li, Xiao-Meng
    DISCRETE MATHEMATICS, 2025, 348 (05)
  • [2] On trees with Laplacian eigenvalue one
    Barik, S.
    Lal, A. K.
    Pati, S.
    LINEAR & MULTILINEAR ALGEBRA, 2008, 56 (06): : 597 - 610
  • [3] On graphs whose smallest distance (signless Laplacian) eigenvalue has large multiplicity
    Lu, Lu
    Huang, Qiongxiang
    Huang, Xueyi
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (11): : 2218 - 2231
  • [4] On the multiplicity of the least signless Laplacian eigenvalue of a graph
    Tian, Fenglei
    Guo, Shu-Guang
    Wong, Dein
    DISCRETE MATHEMATICS, 2022, 345 (09)
  • [5] The multiplicity of Laplacian eigenvalue two in unicyclic graphs
    Akbari, Saieed
    Kiani, Dariush
    Mirzakhah, Maryam
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 445 : 18 - 28
  • [6] Domination number and Laplacian eigenvalue of trees
    Xue, Jie
    Liu, Ruifang
    Yu, Guanglong
    Shu, Jinlong
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 592 : 210 - 227
  • [7] Domination number and Laplacian eigenvalue of trees
    Xue J.
    Liu R.
    Yu G.
    Shu J.
    Linear Algebra and Its Applications, 2020, 592 : 210 - 227
  • [8] On the second largest Laplacian eigenvalue of trees
    Guo, JM
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 404 : 251 - 261
  • [9] THE MULTIPLICITY OF THE 1ST NONZERO LAPLACIAN EIGENVALUE
    DEVERDIERE, YC
    COMMENTARII MATHEMATICI HELVETICI, 1986, 61 (02) : 254 - 270
  • [10] Nodal sets of Laplacian eigenfunctions with an eigenvalue of multiplicity 2
    Lyons, Andrew
    ANNALES MATHEMATIQUES DU QUEBEC, 2025, 49 (01): : 105 - 153
12345