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

• 作者: Xiao-guo TIAN Li-gong WANG You LU
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 628-644
• 页数: 17页
• 语种: 英文

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 λk(G)be the k-th smallest normalized Laplacian eigenvalue of G.Denote by ρ(A)the spectral radius of the matrix A.In this paper,we study the behaviors of λ2(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)).