A short proof of the odd-girth theorem

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

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Recently, it has been shown that a connected graph Γ with d+1 distinct eigenvalues and odd-girth 2d+1 is distance-regular. The proof of this result was based on the spectral excess theorem. In this note we present an alternative and more direct proof which does not rely on the spectral excess theorem, but on a known characterization of distance regular graphs in terms of the predistance polynomial of degree d.
Original languageEnglish
Pages (from-to)12-16
JournalThe Electronic Journal of Combinatorics: EJC
Volume19
Issue number3
Publication statusPublished - 2012

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Girth
Excess
Odd
Polynomials
Distance-regular Graph
Theorem
Connected graph
Eigenvalue
Distinct
Polynomial
Alternatives

Cite this

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A short proof of the odd-girth theorem. / van Dam, E.R.; Fiol, M.A.

In: The Electronic Journal of Combinatorics: EJC, Vol. 19, No. 3, 2012, p. 12-16.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Fiol, M.A.

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AB - Recently, it has been shown that a connected graph Γ with d+1 distinct eigenvalues and odd-girth 2d+1 is distance-regular. The proof of this result was based on the spectral excess theorem. In this note we present an alternative and more direct proof which does not rely on the spectral excess theorem, but on a known characterization of distance regular graphs in terms of the predistance polynomial of degree d.

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JO - The Electronic Journal of Combinatorics: EJC

JF - The Electronic Journal of Combinatorics: EJC

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