A characterization of the association schemes of Hermitian forms

Let Y=(X, {R_i}_0≦i≦d) be an association scheme whose parameters coincide with those of the association scheme Her (d, q) of Hermitian forms in d-dimen-sional space over the field GF(q²). Suppose that every edge of the distance- regular graph Γ=(X, R₁) is contained in a clique of size q. It is shown that if d≧3 then Y is isomorphic to Her (d, q). In the case d=2 a generalized quadrangle with the parameters (q, q²) is reconstructed from Y.