The non-collinearity graph of the \(O^+(8,2)\) quadric is uniquely geometrisable
type: Item
instance of: scholarly article
title: The non-collinearity graph of the \(O^+(8,2)\) quadric is uniquely geometrisable
zbMATH Open document ID: 0992.05029
DOI: 10.1023/A:1008378226142
author: Pratima Panigrahi
published in: Designs, Codes and Cryptography
publication date: 2001-02-06T00:00:00Z
review text: The non-collinearity graph of the \(O^+(8,2)\) quadric is the graph whose vertex set consists of the points of the \(O^+(8,2)\) polar space, and two vertices are adjacent in this graph if and only if the corresponding points are non-collinear in the polar space. In this paper, the author shows that there is a unique partial geometry \(\text{pg}(8,7,4)\) whose point graph is this graph, and the author also demonstrates that this geometry has the affine plane of order 3 as a subgeometry.
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E14
Mathematics Subject Classification ID: 05C62
zbMATH DE Number: 1515345
zbMATH Keywords: non-collinearity graph
zbMATH Keywords: quadric
zbMATH Keywords: polar space
zbMATH Keywords: partial geometry
zbMATH Keywords: affine plane
reviewed by: Michael Raines
MaRDI profile type: Publication
full work available at URL: a:1008378226142
OpenAlex ID: W1569101916
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description: scientific article; zbMATH DE number 1515345