The Laplacian spectral excess theorem for distance-regular graphs

E.R. van Dam, M.A. Fiol

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

The spectral excess theorem states that, in a regular graph Γ, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of Γ), and Γ is distance-regular if and only if equality holds. In this note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of Γ.
Original languageEnglish
Pages (from-to)245-250
JournalLinear Algebra and its Applications
Volume458
Early online date24 Jun 2014
DOIs
Publication statusPublished - 1 Oct 2014

Keywords

  • Distance-regular graphs
  • spectral excess theorem
  • Laplacian spectrum
  • orthogonal polynomials

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