Classification of three-class association schemes using backtracking with dynamic variable ordering

Abstract

We describe several techniques for the exhaustive computer generation of non-isomorphic association schemes with a given set of intersection numbers using a backtracking algorithm with forward checking and dynamic variable ordering. We have applied these techniques to the classification of certain open parameter sets for three-class association schemes listed by Van Dam in (Three-class association schemes, J. Algebraic Combin. 10 (1999) 69–107) for which we present several new results. Among these are some new (imprimitive) distance regular graphs of diameter 3.