Classical Distance-Regular Graphs of Negative Type

Abstract

We prove the following theorem. \emsp;Theorem.Let Γ=(X, R)denote a distance-regular graph with classical parameters(d, b, α, β)and d≥4.Suppose b 1.Then precisely one of the following(i)-(iii)holds. (i)Γ is the dual polar graph2A2d-1(-b). (ii)Γ is the Hermitian forms graph Her-b(d). (iii)α=(b-1)/2,β=-(1+bd)/2,and-b is a power of an odd prime. © 1999 Academic Press.