Distance Biregular Bipartite Graphs

We describe here some properties of a class of graphs which extends the class of distance regular graphs: our graphs are bipartite and for each vertex there exists an intersection array depending on the stable component of the vertex. Thus our graphs are to distance regular graphs as bipartite regular graphs are to regular graphs. They also are to non-symmetric association schemes as distance regular graphs are to symmetric association schemes. We also give some examples.