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

Xiao guo Tian, Li gong Wang, You Lu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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 to ρ(L(G) ). Meanwhile we characterize all the simple connected graphs with ρ(L(G))=ρ(Q(G)).

Original languageEnglish
Pages (from-to)628-644
Number of pages17
JournalActa Mathematicae Applicatae Sinica
Volume37
Issue number3
DOIs
StatePublished - Jul 2021

Keywords

  • 05C50
  • 15A18
  • normalized Laplacian spectral radius
  • normalized signless Laplacian spectral radius
  • second smallest normalized Laplacian eigenvalue

Fingerprint

Dive into the research topics of 'On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph'. Together they form a unique fingerprint.

Cite this