Maximal -distance sets containing the representation of the Johnson graph

We classify the maximal m -distance sets in R n − 1 which contain the representation of the Johnson graph J ( n , m ) for m = 2 , 3 . Furthermore, we determine the necessary and sufficient condition for n and m such that the representation of the Johnson graph J ( n , m ) is not maximal as an m -distance set. we classify the maximal two-distance sets in R n − 1 which contain the representation of J ( n − 1 , 2 ) .