On the characterization of geometric distance-regular graphs

Abstract

In 2010, Koolen and Bang proposed the following conjecture: For a fixed integer $m\ge 2$, any geometric distance-regular graph with smallest eigenvalue $-m$, diameter $D\ge 3$ and $c_2\ge 2$ is either a Johnson graph, a Grassmann graph, a Hamming graph, a bilinear forms graph, or the number of vertices is bounded above by a function of $m$. In this paper, we obtain some partial results towards this conjecture.

arXiv admin note: substantial text overlap with arXiv:2410.22994