Triangle- and pentagon-free distance-regular graphs with an eigenvalue multiplicity equal to the valency

We also classify bipartite almost 2-homogeneous distance-regular graphs with diameter d⩾4. In particular, we prove that such a graph is either 2-homogeneous (and thus classified by Nomura and Yamazaki), or a folded k-cube for k even, or a generalized 2d-gon with order (1,k-1).