### Abstract

*d*+1 distinct eigenvalues and odd-girth 2

*d*+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 language | English |
---|---|

Pages (from-to) | 12-16 |

Journal | The Electronic Journal of Combinatorics: EJC |

Volume | 19 |

Issue number | 3 |

Publication status | Published - 2012 |

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*The Electronic Journal of Combinatorics: EJC*,

*19*(3), 12-16.

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*The Electronic Journal of Combinatorics: EJC*, vol. 19, no. 3, pp. 12-16.

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

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - A short proof of the odd-girth theorem

AU - van Dam, E.R.

AU - Fiol, M.A.

PY - 2012

Y1 - 2012

N2 - 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.

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.

M3 - Article

VL - 19

SP - 12

EP - 16

JO - The Electronic Journal of Combinatorics: EJC

JF - The Electronic Journal of Combinatorics: EJC

SN - 1097-1440

IS - 3

ER -