Kite-free distance-regular graphs

AbstractLet Γ denote a distance-regular graph with classical parameters (d, b, α, β). Suppose that the diameter d ≥ 3, and suppose that the parameter b (which is known to be an integer) satisfies b < −1. Then we show that Γ does not contain vertices x, y, z and u such that x, y, z are mutually adjacent, and such that u is at distance ∂(u, y) = ∂(u, x) − 1. We conclude that the Hermitean forms graph Her(d,q) is uniquely determined by its intersection numbers if d ≥ 3