Trees with a large Laplacian eigenvalue multiplicity

Saieed Akbari, Edwin van Dam, Mohammadhossein Fakharan

Research output: Contribution to journalArticleScientificpeer-review

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 languageEnglish
Pages (from-to)262-273
JournalLinear Algebra and its Applications
Volume586
DOIs
Publication statusPublished - Feb 2020

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Laplacian Eigenvalues
Largest Eigenvalue
Multiplicity
Algebraic Connectivity
Upper bound
Integer

Keywords

  • Laplacian spectrum
  • trees
  • multiplicities of eigenvalues

Cite this

Akbari, Saieed ; van Dam, Edwin ; Fakharan, Mohammadhossein. / Trees with a large Laplacian eigenvalue multiplicity. In: Linear Algebra and its Applications. 2020 ; Vol. 586. pp. 262-273.
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Trees with a large Laplacian eigenvalue multiplicity. / Akbari, Saieed; van Dam, Edwin; Fakharan, Mohammadhossein.

In: Linear Algebra and its Applications, Vol. 586, 02.2020, p. 262-273.

Research output: Contribution to journalArticleScientificpeer-review

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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.

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KW - multiplicities of eigenvalues

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