Distance-regular graphs with strongly regular subconstituents
type: Item
instance of: scholarly article
title: Distance-regular graphs with strongly regular subconstituents
zbMATH Open document ID: 0879.05073
DOI: 10.1023/A:1008653827221
author: Anna Kasikova
published in: Journal of Algebraic Combinatorics
publication date: 1997-07-23T00:00:00Z
review text: The main result of the article is a theorem about distance-regular graphs of diameter \(d\geq 3\) with all subconstituents being strongly regular graphs. The author shows that these are precisely the Taylor graphs \((d=3\) and \(|\Gamma_3 (u) |=1)\) or graphs with \(a_1= 0\), \(a_i\leq 1\) for \(2\leq i\leq d\). The result nicely complements the classification of strongly regular graphs with strongly regular subconstituents obtained by Cameron, Goethals and Seidel. The proof presented consists of a series of lemmas examining the possible parameters combined with an inventive use of previously known results.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1038957
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: diameter
zbMATH Keywords: strongly regular graphs
reviewed by: Robert Jajcay
MaRDI profile type: Publication
cites work: Q3992965
cites work: Q3218140
cites work: Strongly regular graphs having strongly regular subconstituents
cites work: Q5181734
cites work: The Graph Extension Theorem
cites work: Regular 2-Graphs
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description: scientific article; zbMATH DE number 1038957