The Strongly Regular $(45,12,3,3)$ Graphs

Kris Coolsaet, Jan Degraer, Edward Spence


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 $51840$.

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