Some properties of the distance Laplacian eigenvalues of a graph

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


The distance Laplacian of a connected graph G is defined by (equation presented), where (equation presented) is the distance matrix of G, and Diag(Tr) is the diagonal matrix whose main entries are the vertex transmissions in G. The spectrum of (equation presented) is called the distance Laplacian spectrum of G. In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties of the distance Laplacian spectrum that enable us to derive the distance Laplacian characteristic polynomials for several classes of graphs.

Original languageEnglish
Pages (from-to)751-761
Number of pages11
JournalCzechoslovak Mathematical Journal
Issue number3
Publication statusPublished - Sept 2014
Externally publishedYes


  • Characteristic polynomial
  • Distance matrix
  • Eigenvalue
  • Laplacian

ASJC Scopus subject areas

  • General Mathematics


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