The strongly regular (40, 12, 2, 4) graphs
type: Item
instance of: scholarly article
title: The strongly regular (40, 12, 2, 4) graphs
zbMATH Open document ID: 0940.05072
published in: The Electronic Journal of Combinatorics
publication date: 2000-05-11T00:00:00Z
full work available at URL: https://eudml.org/doc/120390
full work available at URL: v7i1r22.html
review text: Summary: In a previous paper [cf. \textit{E. Spence}, (40, 13, 4) designs derived from strongly regular graphs, Advances in finite geometries and designs, Proc. 3rd Isle of Thorns Conf., Chelwood Gate/UK 1990, 359-368 (1991; Zbl 0760.05007)] it was established that there are at least \(27\) non-isomorphic strongly regular \((40,12,2,4)\) graphs. Using a different and more efficient method we have re-investigated these graphs and have now been able to determine them all, and so complete the classification. We have discovered that there are precisely \(28\) non-isomorphic \((40,12,2,4)\) strongly regular graphs. The one that was not found in the previous investigation is characterised uniquely by the fact that every neighbour graph is triangle-free.
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1446314
zbMATH Keywords: classification
zbMATH Keywords: strongly regular graphs
author: Edward Spence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1446314