The Enumeration of Primitive Commutative Association Schemes with a Non-symmetric Relation of Valency, at Most 4

Abstract

Let (X,G) be an association scheme in the sense of [64] where X is finite. Then (X, g) is a regular digraph for each g ∈ G. It is an interesting problem to find all regular digraphs which might be an element of G under certain hypotheses about intersection numbers or an induced subgraph of the graph, and to determine the whole structure of (X, G).