Geodesic-transitive graphs with large diameter
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910118015139840 |
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| author | Hua, Pei Ce |
| author_facet | Hua, Pei Ce |
| contents | We review the nearly complete classification project for finite distance-transitive graphs and compile a list of all known graphs. Interestingly, we find that those graphs with diameter larger than 4, apart from a small finite number of exceptions, are geodesic-transitive. Their geodesics exhibit a clear (often geometric) structure. On the other hand, we provide examples of graphs that are distance-transitive but not geodesic-transitive, including two infinite families with diameter 3 and a few sporadic ones with diameter 3, 4 or 7. In the last section, we extend our investigation to polar Grassmann graphs and provide an explicit description of their geodesics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04935 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geodesic-transitive graphs with large diameter Hua, Pei Ce Combinatorics We review the nearly complete classification project for finite distance-transitive graphs and compile a list of all known graphs. Interestingly, we find that those graphs with diameter larger than 4, apart from a small finite number of exceptions, are geodesic-transitive. Their geodesics exhibit a clear (often geometric) structure. On the other hand, we provide examples of graphs that are distance-transitive but not geodesic-transitive, including two infinite families with diameter 3 and a few sporadic ones with diameter 3, 4 or 7. In the last section, we extend our investigation to polar Grassmann graphs and provide an explicit description of their geodesics. |
| title | Geodesic-transitive graphs with large diameter |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.04935 |