On the characterization of geometric distance-regular graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914257273094144 |
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| author | Lv, Chenhui Koolen, Jack H. |
| author_facet | Lv, Chenhui Koolen, Jack H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the characterization of geometric distance-regular graphs Lv, Chenhui Koolen, Jack H. Combinatorics 05E30 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. |
| title | On the characterization of geometric distance-regular graphs |
| topic | Combinatorics 05E30 |
| url | https://arxiv.org/abs/2601.10330 |