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：
Acta Mathematicae Applicatae Sinica | 2021年 / 37卷 / 03期
基金：
中央高校基本科研业务费专项资金资助; 中国国家自然科学基金;
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：
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）).
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页码：628 / 644
页数：17
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