A note on triangle-free distance-regular graphs with a(2) not equal 0

Abstract

Let Gamma denote a distance-regular graph with classical parameters (D, b, alpha, beta) and D >= 3. Assume the intersection numbers a(1) = 0 and a(2) not equal 0. We show that the intersection number c(2) is either 1 or 2, and if c(2) = 1, then (b, alpha, beta) = (-2, -2, ((-2)(D+l) - 1)/3). (C) 2008 Elsevier Inc. All rights reserved.