Conference matrices from projective planes of order 9
type: Item
instance of: scholarly article
title: Conference matrices from projective planes of order 9
zbMATH Open document ID: 0568.05012
DOI: 10.1016/S0195-6698(85)80021-4
author: J. J. Seidel
author: Cor Hurkens
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: The four known nonisomorphic projective planes of order 9 determine seven nonismorphic affine planes of order 9. From the corresponding transversal designs T(10,9), one finds \(7\times \left( \begin{matrix} 10\\ 5\end{matrix} \right)=1764\) transversal designs T(5,9). Each of these defines a strongly regular graph with parameters (81,40,19,20), i.e. a so-called half-case s.r.g., and a corresponding conference matrix. It is shown that among these there are 175 nonisomorphic strongly regular graphs and 26 nonequivalent conference matrices. These matrices are given in tables. These results depend on a computer search combined with symmetry arguments and the following theorem. Theorem: If K is a graph on four vertices and G is a half-case s.r.g., then G contains as many copies of K as of its complement.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 3906507
zbMATH Keywords: projective planes of order 9
zbMATH Keywords: transversal designs
zbMATH Keywords: strongly regular graph
zbMATH Keywords: conference matrix
reviewed by: Jack van Lint
MaRDI profile type: Publication
cites work: Q3880871
cites work: Orthogonal Matrices with Zero Diagonal
cites work: Q5683869
cites work: Q4121914
description: scientific article; zbMATH DE number 3906507