The strongly regular (45,12,3,3) graphs. (English) Zbl 1098.05081
Summary: Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters \(v=45\), \(k=12\), \(\lambda=\mu=3\). It turns out that there are \(78\) such graphs, having automorphism groups with sizes ranging from \(1\) to \(51840\).
MSC:
05E30 | Association schemes, strongly regular graphs |
05-04 | Software, source code, etc. for problems pertaining to combinatorics |