The Strongly Regular (40, 12, 2, 4) Graphs

In a previous paper 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. Key words and phrases: Strongly regular graph, classification AMS subject classifications: Primary 05B05. 1 

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Edward Spence
• Keywords: COMBINATORICS 2000, Efficient Method, Regular, Strongly Regular Graph