A bound for the number of columns l(c,a,b) in the intersection array of a distance-regular graph

In this paper we give a bound for the number l(c,a,b) of columns (c,a,b)T in the intersection array of a distance-regular graph. We also show that this bound is intimately related to the Bannai–Ito conjecture

Distance-regular graphs

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page