A classification of two-distance-transitive Cayley graphs over the generalized quaternion groups
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_ | 1866918001517789184 |
|---|---|
| author | Jin, Wei Li, Pingshan Tan, Li |
| author_facet | Jin, Wei Li, Pingshan Tan, Li |
| contents | A non-complete graph is \emph{$2$-distance-transitive} if, for $i=1,2$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance $i$ in the graph, there exists an element of the graph automorphism group that maps $(u_1,v_1)$ to $(u_2,v_2)$. This is a generalization concept of the classical well-known distance-transitive graphs. In this paper, we completely determine the family of $2$-distance-transitive Cayley graphs over the generalized quaternion groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A classification of two-distance-transitive Cayley graphs over the generalized quaternion groups Jin, Wei Li, Pingshan Tan, Li Combinatorics A non-complete graph is \emph{$2$-distance-transitive} if, for $i=1,2$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance $i$ in the graph, there exists an element of the graph automorphism group that maps $(u_1,v_1)$ to $(u_2,v_2)$. This is a generalization concept of the classical well-known distance-transitive graphs. In this paper, we completely determine the family of $2$-distance-transitive Cayley graphs over the generalized quaternion groups. |
| title | A classification of two-distance-transitive Cayley graphs over the generalized quaternion groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.19130 |