Minimum values of the second largest Q-eigenvalue

Mustapha Aouchiche, Issmail El Hallaoui

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


For a graph G, the signless Laplacian matrix Q(G) is defined as Q(G)=D(G)+A(G), where A(G) is the adjacency matrix of G and D(G) the diagonal matrix whose main entries are the degrees of the vertices in G. The Q-spectrum of G is that of Q(G). In the present paper, we are interested in the minimum values of the second largest signless Laplacian eigenvalue q2(G) of a connected graph G. We find the five smallest values of q2(G) over the set of connected graphs G with given order n. We also characterize the corresponding extremal graphs.

Original languageEnglish
Pages (from-to)46-51
Number of pages6
JournalDiscrete Applied Mathematics
Publication statusPublished - Jan 15 2022


  • Extremal graph
  • Lower bound
  • Second largest eigenvalue
  • Signless Laplacian

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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