The Study Of Non-symmetric Association Schemes With Three Classes

In the theory of association schemes, association schemes with small classes have close relations with combinatorial designs and strongly regular graphs. be a association scheme with three classes, is a two-class association scheme. This is equivalent are strongly regular graphs. Therefore, the study of three-class association schemes is reduced to that of their fission schemes with two classes.In the paper, we first study the parametric conditions under which such fissions are feasible, and then use these conditions to investigate the fissions of several families of strongly regular graphs including Paley, symplectic, Latin square and orthogonal graphs. We also explore connections between three-class non-symmetric association schemes and combinatorial designs such as tournaments, Hadamard matrices.