Nonexistence of a class of distance-regular graphs

Let Γ denote a distance-regular graph with diameter D > 3 and intersection numbers a1 = 0; a2 6≠ 0, and c2 = 1. We show a connection between the d-bounded property and the nonexistence of parallelograms of any length up to d+1. Assume further that Γ is with classical parameters (D; b; α ß), Pan and Weng (2009) showed that (b; α; ß) = (-2;-2; ((-2)D+1-1)/3): Under the assumption D > 4, we exclude this class of graphs by an application of the above connection.