Locally Shrikhande graphs and their automorphisms
type: Item
instance of: scholarly article
title: Locally Shrikhande graphs and their automorphisms
zbMATH Open document ID: 0913.05093
DOI: 10.1007/BF02672915
published in: Siberian Mathematical Journal
publication date: 1999-05-11T00:00:00Z
review text: A graph on the vertex set \(X\times Y\) is an \(m\times n\)-graph provided that \((x_1,y_1)\) is adjacent to \((x_2,y_2)\) if and only if \(x_1=x_2\) or \(y_1=y_2\). An \(m\times m\)-graph, called lattice graph, is strongly regular with parameters \(v=m^2\), \(k=2m-2\), \(\lambda=m-2\). A strongly regular graph with parameters \((16,6,2,2)\) is called a Shrikhande graph. The main result consists in describing locally Shrikhande graphs, i.e. graphs all whose neighborhoods of vertices are Shrikhande graphs. (Similar results for locally lattice graphs are already known.) Namely, it is shown that every connected locally Shrikhande graph has either 80 or 40 vertices, and its possible diagrams are represented.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C90
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C85
zbMATH DE Number: 1286306
zbMATH Keywords: lattice graph
zbMATH Keywords: distance
zbMATH Keywords: diameter
zbMATH Keywords: lattice
zbMATH Keywords: forbidden subgraph
zbMATH Keywords: Shrikhande graph
zbMATH Keywords: strongly regular graph
author: Alexandre A. Makhnev
author: Dmitriĭ Viktorovich Paduchikh
MaRDI profile type: Publication
cites work: Diagrams for geometries and groups
cites work: Q3775569
cites work: Q3992965
cites work: Multiple Extensions of Generalized Hexagons Related to the Simple Groups McL and Co3
full work available at URL: https://doi.org/10.1007/bf02672915
OpenAlex ID: W1964597485
description: scientific article; zbMATH DE number 1286306