On Distance-Regular Graphs with Smallest Eigenvalue at Least $-m$

J. H. Koolen, S. Bang

Published 2009-08-14Version 1

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least $-m$, diameter at least three and intersection number $c_2 \geq 2$.