Strongly Regular Graphs from Pseudocyclic Association Schemes

In this paper, we give a construction of strongly regular graphs from pseudocyclic association schemes, which is a common generalization of two constructions given by Fujisaki (2004). Furthermore, we prove that the pseudocyclic association scheme arising from the action of PGL(2, q) to the set of exterior lines in PG(2, q), called the elliptic scheme, under the assumption that \(q=2^m\) $q=2^m$ with m an odd prime satisfies the condition of our new construction. As a consequence, we obtain a new infinite family of strongly regular graphs of Latin square type with non-prime-power number of vertices.