Distance spectra of graphs: A survey

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

255 Citations (Scopus)


In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties.

Original languageEnglish
Pages (from-to)301-386
Number of pages86
JournalLinear Algebra and Its Applications
Publication statusPublished - Oct 1 2014
Externally publishedYes


  • Characteristic polynomial
  • Distance matrix
  • Eigenvalues
  • Graph
  • Largest eigenvalue

ASJC Scopus subject areas

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


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