Delsarte clique graphs

In this paper, we consider the class of Delsarte clique graphs, i.e. the class of distance-regular graphs with the property that each edge lies in a constant number of Delsarte cliques. There are many examples of Delsarte clique graphs such as the Hamming graphs, the Johnson graphs and the Grassmann graphs.Our main result is that, under mild conditions, for given s≥2s≥2 there are finitely many Delsarte clique graphs which contain Delsarte cliques with size s+1s+1. Further we classify the Delsarte clique graphs with small ss.