Almost-bipartite distance-regular graphs with the Q-polynomial property

Abstract

Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4 . Assume that the intersection numbers of Γ satisfy a i = 0 for 0 ≤ i ≤ D − 1 and a D ≠ 0 . We show that Γ is a polygon, a folded cube, or an Odd graph.