Trees with a large Laplacian eigenvalue multiplicity

Saieed Akbari, Edwin R. van Dam, Mohammadhossein Fakharan

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


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
Number of pages12
JournalLinear Algebra and its Applications
Publication statusPublished - Feb 2020


  • Laplacian spectrum
  • trees
  • multiplicities of eigenvalues


Dive into the research topics of 'Trees with a large Laplacian eigenvalue multiplicity'. Together they form a unique fingerprint.

Cite this