On regular Terwilliger graphs with \(\mu=2\)
type: Item
instance of: scholarly article
title: On regular Terwilliger graphs with \(\mu=2\)
zbMATH Open document ID: 0874.05062
DOI: 10.1007/BF02110729
published in: Siberian Mathematical Journal
publication date: 1997-11-09T00:00:00Z
review text: The monograph [\textit{A. E. Brouwer}, \textit{A. M. Cohen} and \textit{A. Neumaier}, Distance-regular graphs, Springer, Berlin (1989; Zbl 0747.05073)] put the following problem: Is it true that a connected regular Terwilliger graph is either the \(\mu\)-extension of some graph or the subgraph \([a]- K(a)\) is regular for every vertex \(a\) of the graph? (We note that \([a]\) is the neighbourhood of \(a\), and \(K(a)\) is a core of \(a\).) The author solves this problem for \(\mu=2\). More precisely, he proves that a connected regular Terwilliger graph with \(\mu=2\) is either the 2-extension of a graph with \(\mu=1\) or a locally \(\lambda\) graph.
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1023912
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: regular Terwilliger graph
author: Alexandre A. Makhnev
reviewed by: Ferdinand Gliviak
MaRDI profile type: Publication
cites work: Q3992965
cites work: Distance-regular graphs with girth 3 or 4: I
full work available at URL: https://doi.org/10.1007/bf02110729
OpenAlex ID: W1965581394
description: scientific article; zbMATH DE number 1023912