Extending the dual of the Petersen graph
type: Item
instance of: scholarly article
title: Extending the dual of the Petersen graph
zbMATH Open document ID: 0917.05017
author: Thomas Meixner
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/119826
review text: This paper concerns a special class of residually connected geometries of rank 3 with flag-transitive automorphism group. Such a geometry can be described by a diagram in which the types of the rank 2 residues are listed. The class considered here is defined by the following two types of residues. One is a circle geometry in the sense of \textit{F. Buekenhout} [J. Comb. Theory, Ser. A 27, 121-151 (1979; Zbl 0419.51003)], this is the geometry of vertices and edges of a finite complete graph. The other is the geometry dual to that of the Petersen graph. It is shown that each geometry of this class is a quotient of the universal 2-cover of one of the two examples which are described explicitely. The second example should be modified in the following way: lines are the pairs \((l,\pi)\) consisting of a \(2\)-set \(l\) of \(\Psi \) and a partition \(\pi =\{l,m,n\}\) of \(\Psi \) into three pairwise disjoint \(2\)-sets, one of which is equal to \(l\). A plane \(p\) is defined to be incident with the line \((l,\pi)\) if \(p=l\cup m\) or \(p=l\cup n\).
reviewed by: Johann Linhart
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 51E99
zbMATH DE Number: 1266850
zbMATH Keywords: diagram geometry
zbMATH Keywords: flag-transitive group
zbMATH Keywords: Petersen graph
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1266850