Local structure of graphs with \(\lambda= \mu= 2\), \(a_ 2=4\)
type: Item
instance of: scholarly article
title: Local structure of graphs with \(\lambda= \mu= 2\), \(a_ 2=4\)
zbMATH Open document ID: 0837.05093
DOI: 10.1007/BF01192521
published in: Combinatorica
publication date: 1996-01-24T00:00:00Z
review text: The author studies graphs \(G\) with the following properties: \(\lambda = 2\): For any two adjacent vertices in \(G\), there are exactly two vertices adjacent to both. \(\mu = 2\): For any two vertices at distance 2, there are exactly two vertices adjacent to both. \(a_2 = 4\): For any pair of vertices \(p\), \(q\) of \(G\) at distance 2, there are exactly four vertices adjacent to \(q\) and at distance 2 from \(p\). He proves that the graph induced by the set of neighbors of any vertex in \(G\) is a disjoint union of triangles, hexagons or heptagons. This result implies that there is no distance-regular graph with intersection array (13, 10, 7; 1, 2, 7).
reviewed by: Konrad Engel
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 837828
zbMATH Keywords: strongly regular
zbMATH Keywords: Shrikhande graph
zbMATH Keywords: Doob graph
zbMATH Keywords: distance
zbMATH Keywords: distance- regular graph
zbMATH Keywords: intersection array
author: Kris Coolsaet
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01192521
OpenAlex ID: W18439870
description: scientific article; zbMATH DE number 837828