The generalized distance spectrum of a graph and applications

Research output: Contribution to journalArticlepeer-review


The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many of the commonly studied spectra of graphs. We show that for a large class of graphs these eigenvalues can be computed explicitly. We also present the applications of our results to competition models in ecology and rapidly mixing Markov chains.

Original languageEnglish (US)
Pages (from-to)2425-2458
Number of pages34
JournalLinear and Multilinear Algebra
Issue number13
StatePublished - 2022


  • Distance-regular graph
  • Markov chains
  • ecological models
  • spectral graph theory

ASJC Scopus subject areas

  • Algebra and Number Theory


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