Laplacian eigenvalue distribution of a graph with given independence number

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.