Two Laplacians for the distance matrix of a graph

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

195 Citations (Scopus)


We introduce a Laplacian and a signless Laplacian for the distance matrix of a connected graph, called the distance Laplacian and distance signless Laplacian, respectively. We show the equivalence between the distance signless Laplacian, distance Laplacian and the distance spectra for the class of transmission regular graphs. There is also an equivalence between the Laplacian spectrum and the distance Laplacian spectrum of any connected graph of diameter 2. Similarities between n, as a distance Laplacian eigenvalue, and the algebraic connectivity are established.

Original languageEnglish
Pages (from-to)21-33
Number of pages13
JournalLinear Algebra and Its Applications
Issue number1
Publication statusPublished - Jun 1 2013
Externally publishedYes


  • Distance matrix
  • Eigenvalues
  • Graph
  • Laplacian
  • Signless Laplacian

ASJC Scopus subject areas

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


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