The Laplacian spectral excess theorem for distance-regular graphs

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

Research output: Contribution to journalArticleScientificpeer-review

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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

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Distance-regular Graph
Excess
Theorem
Laplacian Spectrum
Adjacency
Regular Graph
Equality
Regularity
If and only if
Vertex of a graph

Keywords

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

Cite this

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The Laplacian spectral excess theorem for distance-regular graphs. / van Dam, E.R.; Fiol, M.A.

In: Linear Algebra and its Applications, Vol. 458, 01.10.2014, p. 245-250.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Fiol, M.A.

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KW - Laplacian spectrum

KW - orthogonal polynomials

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