Maximal mm-distance sets containing the representation of the Johnson graph J(n,m)J(n,m)

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