The complete classification of triply-transitive strongly regular graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917045636956160 |
|---|---|
| author | Li, Weicong Zou, Hanlin |
| author_facet | Li, Weicong Zou, Hanlin |
| contents | This paper completes the classification of triply-transitive strongly regular graphs, a program recently initiated by Herman, Maleki, and Razafimahatratra. By proving that the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ and the affine polar graph $\mathrm{VO}^{\varepsilon}_{2m}(2)$ are triply-transitive, we resolve the final open cases in the classification. The result is a definitive list of all strongly regular graphs that exhibit this exceptional form of local symmetry, characterized by the equality $T_{0,ω}=T_ω=\widetilde{T}_ω$ of their Terwilliger algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The complete classification of triply-transitive strongly regular graphs Li, Weicong Zou, Hanlin Combinatorics 05E30, 05C25, 20B25, 51E99 This paper completes the classification of triply-transitive strongly regular graphs, a program recently initiated by Herman, Maleki, and Razafimahatratra. By proving that the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ and the affine polar graph $\mathrm{VO}^{\varepsilon}_{2m}(2)$ are triply-transitive, we resolve the final open cases in the classification. The result is a definitive list of all strongly regular graphs that exhibit this exceptional form of local symmetry, characterized by the equality $T_{0,ω}=T_ω=\widetilde{T}_ω$ of their Terwilliger algebras. |
| title | The complete classification of triply-transitive strongly regular graphs |
| topic | Combinatorics 05E30, 05C25, 20B25, 51E99 |
| url | https://arxiv.org/abs/2510.23441 |