On Lichnerowicz sharp distance-regular graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910018653126656 |
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| author | Chen, Kaizhe Liu, Shiping Zhang, Heng |
| author_facet | Chen, Kaizhe Liu, Shiping Zhang, Heng |
| contents | The first non-zero Laplacian eigenvalue $λ_1$ of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature $κ$. This is a discrete analogue of the classical Lichnerowicz Theorem. A graph with $λ_1=κ$ is called Lichnerowicz sharp. In this note, we completely classify all Lichnerowicz sharp distance-regular graphs. Our result substantially strengthens the corresponding classification by Cushing, Kamtue, Koolen, Liu, Münch, and Peyerimhoff (Adv. Math. 2020), which required an extra spectral condition. As a key preparatory step, we provide a classification of all amply regular Terwilliger graphs with positive Lin-Lu-Yau curvature, a result that is interesting of its own right. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Lichnerowicz sharp distance-regular graphs Chen, Kaizhe Liu, Shiping Zhang, Heng Combinatorics The first non-zero Laplacian eigenvalue $λ_1$ of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature $κ$. This is a discrete analogue of the classical Lichnerowicz Theorem. A graph with $λ_1=κ$ is called Lichnerowicz sharp. In this note, we completely classify all Lichnerowicz sharp distance-regular graphs. Our result substantially strengthens the corresponding classification by Cushing, Kamtue, Koolen, Liu, Münch, and Peyerimhoff (Adv. Math. 2020), which required an extra spectral condition. As a key preparatory step, we provide a classification of all amply regular Terwilliger graphs with positive Lin-Lu-Yau curvature, a result that is interesting of its own right. |
| title | On Lichnerowicz sharp distance-regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.10396 |