A note on distance-regular graphs with a small number of vertices compared to the valency

In this note we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given alpha > 2, there are finitely many distance-regular graphs Gamma with valency k, diameter D >= 3 and v vertices satisfying v = 3, diameter D >= 3 and C-2 >= epsilon k for a given 0 < epsilon < 1 unless (D = 3 and Gamma is imprimitive) or (D = 4 and Gamma is antipodal and bipartite). Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.X1155sciescopu

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