Trees with a large Laplacian eigenvalue multiplicity

Saieed Akbari; Edwin R. van Dam; Mohammadhossein Fakharan

doi:10.1016/j.laa.2019.10.011

Trees with a large Laplacian eigenvalue multiplicity

Saieed Akbari, Edwin R. van Dam, Mohammadhossein Fakharan

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Abstract

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 , and emphasize the particular role of the algebraic connectivity.

Original language	English
Pages (from-to)	262-273
Number of pages	12
Journal	Linear Algebra and its Applications
Volume	586
DOIs	https://doi.org/10.1016/j.laa.2019.10.011
Publication status	Published - Feb 2020

Keywords

Laplacian spectrum
trees
multiplicities of eigenvalues

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10.1016/j.laa.2019.10.011

https://arxiv.org/abs/1907.11482

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title = "Trees with a large Laplacian eigenvalue multiplicity",

abstract = "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 , and emphasize the particular role of the algebraic connectivity.",

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AU - van Dam, Edwin R.

AU - Fakharan, Mohammadhossein

PY - 2020/2

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N2 - 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 , and emphasize the particular role of the algebraic connectivity.

AB - 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 , and emphasize the particular role of the algebraic connectivity.

KW - Laplacian spectrum

KW - trees

KW - multiplicities of eigenvalues

U2 - 10.1016/j.laa.2019.10.011

DO - 10.1016/j.laa.2019.10.011

M3 - Article

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VL - 586

SP - 262

EP - 273

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Trees with a large Laplacian eigenvalue multiplicity

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