## ABSTRACT

An association scheme with d classes on the set X is a set of d graphs G
_{1},…,G_{d}
with vertex set X such that

if x and y are distinct elements of X, there is exactly one graph G_{i}
in which xy is an edge,

for all x and y from X, and for all i and j from {1,…, d}, the number of elements z such that xz ∈ E(G_{i}
) and yz ∈ E(G_{j}
) is determined by the graph G_{k}
in which xy lies.