The triangular extensions of a generalized quadrangle of order \((3,3)\)
type: Item
instance of: scholarly article
title: The triangular extensions of a generalized quadrangle of order \((3,3)\)
zbMATH Open document ID: 0854.51005
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/222554
review text: A triangular extended generalized quadrangle of order \((s,t)\) can be defined as a graph \(\Gamma\) such that for each vertex \(u\) of \(\Gamma\) the subgraph \(\Gamma (u)\) induced on the neighbourhood of \(u\) is isomorphic to the collinearity graph of a generalized quadrangle of order \((s,t)\). It is known that if \(u\) and \(v\) are vertices at distance two then \(\Gamma (u) \cap \Gamma (v)\) is a hyperoval in \(\Gamma (u)\). The author determines all hyperovals in the two generalized quadrangles of order (3,3) by a computer search and uses this classification to show that there is precisely one triangular extended generalized quadrangle of order (3,3).
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 856772
zbMATH Keywords: triangular extension
zbMATH Keywords: generalized quadrangle
zbMATH Keywords: hyperovals
author: Dmitrii V. Pasechnik
describes a project that uses: nauty
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 856772