On the second largest Laplacian eigenvalues of graphs

Jianxi Li*, Ji Ming Guo, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.

Original languageEnglish
Pages (from-to)2438-2446
Number of pages9
JournalLinear Algebra and Its Applications
Volume438
Issue number5
DOIs
Publication statusPublished - 1 Mar 2013

Scopus Subject Areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Graph
  • Laplacian separator
  • Second largest Laplacian eigenvalue

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