The collinearity graph of the \(O^-(8,2)\) quadric is not geometrisable
type: Item
instance of: scholarly article
title: The collinearity graph of the \(O^-(8,2)\) quadric is not geometrisable
zbMATH Open document ID: 0893.51006
DOI: 10.1023/A:1008234630713
author: Pratima Panigrahi
published in: Designs, Codes and Cryptography
publication date: 1998-07-24T00:00:00Z
review text: The author proves a conjecture of the reviewer and \textit{V. D. Tonchev} [Sankhyā, Ser. A 54, Spec. Vol., 137-145 (1992; Zbl 0883.51003)], that the collinearity graph of the elliptic quadric in \(\text{PG}(7,2)\) is not geometric. By considering the three hyperplanes through a \(\text{PG}(5,2)\) that intersects the quadric in a hyperbolic quadric, the graph can be split in 4 disjoint subgraphs, one of them being the line graph of \(\text{PG}(3,2)\), while the other three graphs are the complements of the triangular graph T(8). The author uses this fact to give a nice combinatorial and computer-free proof of the conjecture.
Mathematics Subject Classification ID: 51E14
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1115734
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: partial geometries
zbMATH Keywords: geometric graphs
zbMATH Keywords: collinearity graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1115734