Association schemes generated by a non-symmetric relation of valency 2 Original Research Article

We give some observations on association schemes with a relation of valency 2 from the representation theory of Bose–Mesner algebras and the basic structure theory. One of the applications of these observations is the classification of the association schemes with a non-symmetric relation of valency 2 if the cardinality of the point set is a product of two primes, and another is the proof of Liʹs conjecture that any finite simple group is a connected 2-DCI-group.