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Laplacian eigenvalue distribution of a graph with given independence number
- Authors
- Choi, Jinwon; Suil, O.; Park, Jooyeon; Wang, Zhiwen
- Issue Date
- 1-Jul-2023
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Laplacian eigenvalues; Independence number
- Citation
- APPLIED MATHEMATICS AND COMPUTATION, v.448
- Journal Title
- APPLIED MATHEMATICS AND COMPUTATION
- Volume
- 448
- ISSN
- 0096-3003
1873-5649
- Abstract
- For a graph G , let alpha(G) be the independence number of G , let L(G) be the Laplacian matrix of G , and let mGI be the number of eigenvalues of L(G) in the interval I. Ahanjideh, Akbari, Fakharan and Trevisan proved that alpha(G) <= mG[0, n - alpha(G)] if G is an n-vertex connected graph. Choi, Moon and Park characterized graphs with alpha(G) = mG[0, n - alpha(G)] for alpha(G) = 2 and alpha (G) = n - 2 . In this paper, we give a characterization for alpha (G) = 3 and alpha (G) = n - 3 .(c) 2023 Elsevier Inc. All rights reserved.
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