On the distance signless Laplacian of a graph

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


The distance signless Laplacian of a connected graph (Formula presented.) is defined by (Formula presented.) , where (Formula presented.) is the distance matrix of (Formula presented.) , and (Formula presented.) is the diagonal matrix whose main entries are the vertex transmissions in (Formula presented.). The spectrum of (Formula presented.) is called the distance signless Laplacian spectrum of (Formula presented.). In the present paper, we study some properties of the distance signless Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance signless Laplacian eigenvalues. We prove several bounds on (Formula presented.) eigenvalues and establish a relationship between (Formula presented.) being a distance signless Laplacian eigenvalue of (Formula presented.) and (Formula presented.) containing a bipartite component.

Original languageEnglish
Pages (from-to)1113-1123
Number of pages11
JournalLinear and Multilinear Algebra
Issue number6
Publication statusPublished - Jun 2 2016
Externally publishedYes


  • Distance matrix
  • Laplacian
  • eigenvalues
  • signless Laplacian
  • spectral radius

ASJC Scopus subject areas

  • Algebra and Number Theory


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