On the extremal values of the second largest q-eigenvalue

Mustapha Aouchiche, Pierre Hansen, Claire Lucas

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue.

Original languageEnglish
Pages (from-to)2591-2606
Number of pages16
JournalLinear Algebra and Its Applications
Issue number10
Publication statusPublished - Nov 15 2011
Externally publishedYes


  • Critical graph
  • Extremal graph
  • Second largest eigenvalue
  • Signless Laplacian

ASJC Scopus subject areas

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


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