Kite-free distance-regular graphs
type: Item
instance of: scholarly article
title: Kite-free distance-regular graphs
zbMATH Open document ID: 0829.05059
DOI: 10.1016/0195-6698(95)90020-9
author: Paul Terwilliger
published in: European Journal of Combinatorics
publication date: 1996-01-07T00:00:00Z
review text: Let \(G\) be a distance-regular graph with classical parameters \((d,b, \alpha, \beta)\). A kite of length \(i\) of \(G\) is a 4-tuple \((x, y, z, u)\) of vertices such that \(x\), \(y\) and \(z\) are mutually adjacent, and \(u\) is at distance \(d(u,x) = i\), and \(d(u,y) = d(u,z) = i - 1\), where \(2 \leq i \leq d\) and \(d\) is the diameter of \(G\). This paper shows that \(G\) contains no kite of length \(i\) for all \(2 \leq i \leq d\) if \(d \geq 3\) and \(b < -1\). Using this result the Hermitian forms graph \(\text{Her} (d,q)\) can be uniquely determined only by its intersection numbers, which improves a result of Ivanov and Shpectorov concerning the Hermitian forms graph \(\text{Her}(d,q)\).
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 790744
zbMATH Keywords: distance-regular graph
zbMATH Keywords: kite
zbMATH Keywords: diameter
zbMATH Keywords: Hermitian forms graph
zbMATH Keywords: intersection numbers
reviewed by: Zhenhong Liu
MaRDI profile type: Publication
full work available at URL: 0195-6698(95)90020-9
OpenAlex ID: W2034093529
cites work: Q3218140
cites work: The graphs with spectral radius between 2 and \(\sqrt{2+\sqrt{5}}\)
cites work: A characterization of the association schemes of Hermitian forms
cites work: A characterization of \(P\)- and \(Q\)-polynomial association schemes
cites work: The subconstituent algebra of an association scheme. I
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description: scientific article; zbMATH DE number 790744