On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph

被引：0

作者：

Xiao-guo TIAN ^{[1
]}

Li-gong WANG ^{[1
,2
]}

You LU ^{[1
]}

机构：

[1] Department of Applied Mathematics, School of Science, Northwestern Polytechnical University

[2] Xi'an-Budapest Joint Research Center for Combinatorics, Northwestern Polytechnical University

来源：

ActaMathematicaeApplicataeSinica | 2021年 / 37卷 / 03期

基金：

中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;

关键词：

second smallest normalized Laplacian eigenvalue; normalized Laplacian spectral radius; normalized signless Laplacian spectral radius;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

Let G be a simple connected graph with order n.Let L（G） and Q（G） be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Let λ;（G） be the k-th smallest normalized Laplacian eigenvalue of G.Denote by p（A） the spectral radius of the matrix A.In this paper,we study the behaviors of λ;（G） and ρ(L（G）) when the graph is perturbed by three operations.We also study the properties of ρ(L（G）) and X for the connected bipartite graphs,where X is a unit eigenvector of L（G） corresponding toρ(L（G）).Meanwhile we characterize all the simple connected graphs with ρ(L（G）)=ρ(Q（G）).

引用

页码：628 / 644

页数：17