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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04935 |
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Table of 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.