The distance-regular graphs with intersection number \(a_1\neq 0\) and with an eigenvalue \(-1-(b_1/2)\)
type: Item
instance of: scholarly article
title: The distance-regular graphs with intersection number \(a_1\neq 0\) and with an eigenvalue \(-1-(b_1/2)\)
zbMATH Open document ID: 0910.05041
DOI: 10.1007/PL00009818
published in: Combinatorica
publication date: 1999-03-14T00:00:00Z
review text: The author refines \textit{P. Terwilliger}'s earlier result in [Discrete Math. 61, 311-315 (1986; Zbl 0606.05045)] that says if the intersection number \(b_1 \not = 0\) for a distance-regular graph, then all eigenvalues are equal to or greater than \(-(b_1/2)-1\). The distance-regular graphs of non-zero intersection number and with eigenvalue \(-(b_1/2)-1\) are listed.
reviewed by: András Pluhár
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1261228
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: eigenvalues
zbMATH Keywords: intersection number
author: Jack H. Koolen
MaRDI profile type: Publication
full work available at URL: pl00009818
OpenAlex ID: W2579546455
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description: scientific article; zbMATH DE number 1261228