The strongly regular (40, 12, 2, 4) graphs
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.
scientific article; zbMATH DE number 1446314