Laplacian eigenvalue distribution of a graph with given independence number

Jinwon Choi, Suil O, Jooyeon Park and Zhiwen Wang

Applied Mathematics and Computation, 2023, vol. 448, issue C

Abstract: For a graph G, let α(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 α(G)≤mG[0,n−α(G)] if G is an n-vertex connected graph. Choi, Moon and Park characterized graphs with α(G)=mG[0,n−α(G)] for α(G)=2 and α(G)=n−2. In this paper, we give a characterization for α(G)=3 and α(G)=n−3.

Keywords: Laplacian eigenvalues; Independence number (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001121

DOI: 10.1016/j.amc.2023.127943

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