The association schemes of dual polar spaces of type [formula omitted] are characterized by their parameters if d⩾3

Abstract

It is shown that the cliques in a distance-regular graph Γ whose parameters are that of the dual polar space graph of type 2A 2d-1(p f) have size p f + 1. This means that Γ is the point graph of a regular near 2 d-gon. If d = 2, we obtain the well-known result due to P.J. Cameron, J.M. Goethals, and J.J. Seidel that a pseudogeometric graph with parameters of the point graph of a generalized quadrangle of type ( q, q 2) is geometric. If d⩾3, then some results due to P.J. Cameron, E.E. Shult, A. Yanushka, and J. Tits on near 2 d-gons imply that Γ coincides with the dual polar space graph of type 2A 2d-1(p f) .