The spectral excess theorem for distance-regular graphs: a global (over)view
type: Item
instance of: scholarly article
title: The spectral excess theorem for distance-regular graphs: a global (over)view
zbMATH Open document ID: 1180.05130
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/117273
full work available at URL: v15i1r129.html
review text: Summary: Distance-regularity of a graph is in general not determined by the spectrum of the graph. The spectral excess theorem states that a connected regular graph is distance-regular if for every vertex, the number of vertices at extremal distance (the excess) equals some given expression in terms of the spectrum of the graph. This result was proved by \textit{M.A. Fiol} and \textit{E. Garriga} [``From local adjacency polynomials to locally pseudo-distance-regular graphs'', J. Comb. Theory, Ser. B 71, No.\,2, 162--183 (Zbl 0888.05056)] using a local approach. This approach has the advantage that more general results can be proven, but the disadvantage that it is quite technical. The aim of the current paper is to give a less technical proof by taking a global approach.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 5541034
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: eigenvalues of graphs
zbMATH Keywords: spectral excess theorem
author: Edwin R. Van Dam
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5541034