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Trees with a large Laplacian eigenvalue multiplicity

Akbari,Saieed
; 
van Dam,Edwin R.
; 
Fakharan,Mohammadhossein
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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Publisher Copyright: © 2019 Elsevier Inc.
Date
2020-02
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Tilburg University Research Output Collection
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Keywords
Laplacian spectrum, trees, multiplicities of eigenvalues
Citation
Akbari, S, van Dam, E R & Fakharan, M 2020, 'Trees with a large Laplacian eigenvalue multiplicity', Linear Algebra and its Applications, vol. 586, pp. 262-273. https://doi.org/10.1016/j.laa.2019.10.011
URI
https://hdl.handle.net/20.500.14602/72235
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