A family of multiply extended grids
type: Item
instance of: scholarly article
title: A family of multiply extended grids
zbMATH Open document ID: 0865.05048
DOI: 10.1007/BF01858461
author: Thomas Meixner
author: Antonio Pasini
published in: Graphs and Combinatorics
publication date: 1997-06-29T00:00:00Z
review text: The paper deals with an infinite family \((\Gamma_n)^\infty_{n=5}\) of finite connected graphs \(\Gamma_n\) that are multiple extensions of the well-known ``extended grid,'' a locally 4-by-4 grid graph discovered by \textit{A. Blokhuis} and \textit{A. E. Brouwer} [J. Graph Theory 13, No. 2, 229-244 (1989; Zbl 0722.05054)]. For \(n>5\), the graphs \(\Gamma_n\) are locally \(\Gamma_{n-1}\) and have the following properties: the automorphism group \(G(n)\) of \(\Gamma_n\) acts transitively on the maximal cliques (which are of order \(n\)), and the stabilizer of some \(n\)-clique \(\pi\) of \(\Gamma_n\) induces \(\Sigma_n\) on the vertices of \(\pi\). The clique complex of \(\Gamma_n\) is shown to be simply connected.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 934040
zbMATH Keywords: flag-transitive geometry
zbMATH Keywords: locally grid graph
zbMATH Keywords: extended grid
zbMATH Keywords: automorphism group
zbMATH Keywords: maximal cliques
zbMATH Keywords: stabilizer
zbMATH Keywords: clique complex
reviewed by: Martin Škoviera
MaRDI profile type: Publication
cites work: Locally 4‐by‐4 grid graphs
cites work: Some extensions and embeddings of near polygons
cites work: Q4276294
description: scientific article; zbMATH DE number 934040