A short proof of the odd-girth theorem
type: Item
instance of: scholarly article
title: A short proof of the odd-girth theorem
zbMATH Open document ID: 1253.05098
published in: The Electronic Journal of Combinatorics
publication date: 2012-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.0153
full work available at URL: v19i3p12
review text: Summary: Recently, it has been shown that a connected graph \(\Gamma\) 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 \(d\).
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 6098354
zbMATH Keywords: eigenvalues of graphs
zbMATH Keywords: distance-regular graphs
author: Edwin R. Van Dam
author: Miquel Angel Fiol
MaRDI profile type: Publication
arXiv ID: 1205.0153
description: scientific article; zbMATH DE number 6098354