A relationship between the diameter and the intersection number c 2 for a distance-regular graph

In this paper we will look at the relationship between the intersection number c ₂ and the diameter of a distance-regular graph. We also give some tools to show that a distance-regular graph with large c ₂ is bipartite, and a tool to show that if k _D is too small then the distance-regular graph has to be antipodal.