A new family of distance-regular graphs and the {0, 1, 2}-cliques in dual polar graphs

Let G be a dual polar graph of type Bd(q) orCd(q). Define a graph Gˆ on the same vertex set by having vertices x and y adjacent in Gˆ if they are of distance 1 or 2 in G. The graph Gˆ was recently shown to be distance-regular [10, 12]. In fact, Gˆ is the halved graph of a bipartite distance-regular graph. When G is of type Cd(q) and q is odd, this bipartite graph is new.