  In this paper we give a lower bound for the least distortion embedding of a
distance regular graph into Euclidean space. We use the lower bound for finding
the least distortion for Hamming graphs, Johnson graphs, and all strongly
regular graphs. Our technique involves semidefinite programming and exploiting
the algebra structure of the optimization problem so that the question of
finding a lower bound of the least distortion is reduced to an analytic
question about orthogonal polynomials.
