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arXiv · 2601.10330

On the characterization of geometric distance-regular graphs

Chenhui Lv·Jack H. Koolen
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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.

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Chenhui Lv, Jack H. Koolen. 2026-01-15. On the characterization of geometric distance-regular graphs. https://arxiv.org/abs/2601.10330

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