Trees with a large Laplacian eigenvalue multiplicity
| Autor: | M.H. Fakharan, E.R. van Dam, Saieed Akbari |
|---|---|
| Přispěvatelé: | Econometrics and Operations Research, Research Group: Operations Research |
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Algebraic connectivity Algebra and Number Theory Laplacian spectrum 010102 general mathematics Multiplicity (mathematics) Eigenvalue multiplicity 010103 numerical & computational mathematics trees Mathematics::Spectral Theory 01 natural sciences Upper and lower bounds Laplacian eigenvalues Combinatorics multiplicities of eigenvalues FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Geometry and Topology Combinatorics (math.CO) 0101 mathematics Laplace operator Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications, 586, 262-273. Elsevier Inc. |
| ISSN: | 0024-3795 |
| DOI: | 10.48550/arxiv.1907.11482 |
| Popis: | 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 $\frac{n-3}{2}$, and emphasize the particular role of the algebraic connectivity. Comment: 11 pages, 5 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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