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For p an odd prime, let Ap be the complete classical affine association scheme whose associate classes correspond to parallel classes of lines in the classical affine plane AG(2, p). It is known that Ap is an amorphic association scheme. We investigate rank 3 fusion schemes of Ap whose basis graphs have the same parameters as the Paley graphs P (p 2 ). In contrast to the Paley graphs, the great majority of graphs we detect are non-self-complementary and non-Schurian. In particular, existence of non-self-complementary graphs with Paley parameters is established for p ≥ 17, with an analogous existence result for non-Schurian such graphs when p ≥ 11. We demonstrate that the number of self-complementary and non-self-complementary strongly regular graphs with Paley parameters grows rapidly as p → ∞.

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