Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

作     者：Jürgen Jost Raffaella Mulas Florentin Münch 

作者机构：Max Planck Institute for Mathematics in the SciencesLeipzigGermany 

出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)

年 卷 期：2022年第10卷第3期

页      面：371-381页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Open access funding provided by Project DEAL 

主　　题：Spectral graph theory Normalized Laplacian Largest eigenvalue Sharp bounds 

摘      要：We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size n−1/*** the same method,we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree,provided this is at most n−1/2.