On the characterization of geometric distance-regular graphs
Abstract
In 2010, Koolen and Bang proposed the following conjecture: For a fixed integer $m \geq 2$, any geometric distance-regular graph with smallest eigenvalue $-m$, diameter $D \geq 3$ and $c_2 \geq 2$ 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.
Fields of Study & Subjects
Finite Group Theory Research
Graph theory and applications
Advanced Graph Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint