Trees with a large Laplacian eigenvalue multiplicity

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2019.10.011
  3. Publisher: Elsevier Inc , 2020
  4. Abstract:
  5. 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 [Formula presented], and emphasize the particular role of the algebraic connectivity. © 2019 Elsevier Inc
  6. Keywords:
  7. Laplacian spectrum ; Multiplicities of eigenvalues ; Trees ; Forestry ; Laplace transforms ; Algebraic connectivity ; Eigenvalues ; Laplacian eigenvalues ; Laplacian spectra ; Non integrals ; Upper Bound ; Eigenvalues and eigenfunctions
  8. Source: Linear Algebra and Its Applications ; Volume 586 , 2020 , Pages 262-273
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379519304458