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      Trees with a large Laplacian eigenvalue multiplicity

      , Article Linear Algebra and Its Applications ; Volume 586 , 2020 , Pages 262-273 Akbari, S ; van Dam, E. R ; Fakharan, M. H ; Sharif University of Technology
      Elsevier Inc  2020
      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 [Formula presented], and emphasize the particular role of the algebraic connectivity. © 2019 Elsevier Inc  
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