3-bounded property in a triangle-free distance-regular graph

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 Gamma is 3-bounded in the sense of the article [C. Weng, D-bounded distance-regular graphs, European Journal of Combinatorics 18 (1997) 211-229]. (c) 2007 Elsevier Ltd. All rights reserved.