On graphs in which the neighborhood of each vertex is isomorphic to the Higman-Sims graph
type: Item
instance of: scholarly article
title: On graphs in which the neighborhood of each vertex is isomorphic to the Higman-Sims graph
zbMATH Open document ID: 1236.05132
DOI: 10.1134/S1064562411040119
author: M. L. Kardanova
author: Alexandre A. Makhnev
author: Dmitriĭ Viktorovich Paduchikh
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: Let \(\Gamma\) be a simple graph and \(a\) be a fixed vertex in \(\Gamma\). Let \(\Gamma_i(a)\) denote the \(i\)-neighborhood of \(a\), i.e., the subgraph induced by \(\Gamma\) on the set of all vertices that are at distance \(i\) from \(a\). \(\Gamma\) is called an amply regular graph with parameters \((v,k,\lambda,\mu)\) if \(\Gamma\) is a regular graph of degree \(k\) on \(v\) vertices in which each edge lies in \(\lambda\) triangles and \(\Gamma_1(a) \cup \Gamma_1(b)\) contains \(\mu\) vertices for any two vertices \(a\) and \(b\) separated by a distance of \(2\) in \(\Gamma\). An amply regular graph of distance \(2\) is called a strongly regular graph. A strongly regular graph with parameters \((100,22,0,6)\) is called Higman-Sims graph. In this work all connected amply regular graphs in which the neighborhoods of the vertices are isomorphic to the Higman-Sims graph are described.
reviewed by: Mirko Lepović
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 5998440
zbMATH Keywords: strongly regular graph
zbMATH Keywords: amply regular graph
zbMATH Keywords: Higman-Sims graph
MaRDI profile type: Publication
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full work available at URL: s1064562411040119
OpenAlex ID: W1968888989
description: scientific article; zbMATH DE number 5998440