A root graph that is locally the line graph of the Petersen graph
type: Item
instance of: scholarly article
title: A root graph that is locally the line graph of the Petersen graph
zbMATH Open document ID: 1023.05135
DOI: 10.1016/S0012-365X(02)00546-0
author: Andries E. Brouwer
author: Jack H. Koolen
author: Mikhail H. Klin
published in: Discrete Mathematics
publication date: 2003-04-09T00:00:00Z
review text: The authors construct a root graph on \(192\) vertices that is locally the line graph of the Petersen graph and they show that this graph is the unique root graph with \(\mu = 2\) that is locally the line graph of the Petersen graph (\(\mu = 2\) means that every two vertices at distance two have precisely two common neighbours). Moreover, a new distance-regular graph on \(96\) vertices (with intersection array \(\{15,10,1;1,2,15\}\) and automorphism group \(2^4 \text{Sym}(6)\)) and several new strongly regular graphs (with parameters \((v,k,\lambda,\mu) = (96,20,4,4)\) and \((96,19,2,4)\)) and square \(2\)-\((96,20,4)\) designs are constructed.
reviewed by: Barbara Baumeister
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05E20
zbMATH DE Number: 1896019
zbMATH Keywords: distance-regular graph
zbMATH Keywords: strongly regular graph
zbMATH Keywords: symmetric design
zbMATH Keywords: local characterization
describes a project that uses: nauty
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1896019