An edge-separating theorem on the second smallest normalized laplacian eigenvalue of a graph and its applications

Jianxi Li*, Ji Ming Guo, Wai Chee SHIU, An Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on λ2(G) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ2(G)≥1-22. Moreover, the trees and unicyclic graphs with λ2(G)=1-22 are also determined, respectively.

Original languageEnglish
Pages (from-to)104-115
Number of pages12
JournalDiscrete Applied Mathematics
Volume171
DOIs
Publication statusPublished - 10 Jul 2014

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • Edge-separating
  • Second smallest normalized Laplacian eigenvalue
  • Tree
  • Unicyclic graph

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