On arc-transitive inner-automorphic Cayley graphs on dihedral groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918429890445312 |
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| author | Huang, Jun-Jie Xie, Jin-Hua |
| author_facet | Huang, Jun-Jie Xie, Jin-Hua |
| contents | A Cayley graph $\Cay(G,S)$ is said to be inner-automorphic if $S$ is a union of conjugacy classes of a group $G$, and arc-transitive if its full automorphism group acts transitively on the set of arcs. In this paper, we characterize four well-known families of arc-transitive graphs that arise as connected inner-automorphic Cayley graphs on dihedral groups, and we provide a necessary condition for other connected arc-transitive Cayley graphs on dihedral groups to be inner-automorphic. We further construct an infinite family of examples satisfying this condition, thereby demonstrating the existence of such graphs. Finally, we complete the classification of all 2-distance-transitive connected inner-automorphic Cayley graphs on dihedral groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On arc-transitive inner-automorphic Cayley graphs on dihedral groups Huang, Jun-Jie Xie, Jin-Hua Group Theory Combinatorics A Cayley graph $\Cay(G,S)$ is said to be inner-automorphic if $S$ is a union of conjugacy classes of a group $G$, and arc-transitive if its full automorphism group acts transitively on the set of arcs. In this paper, we characterize four well-known families of arc-transitive graphs that arise as connected inner-automorphic Cayley graphs on dihedral groups, and we provide a necessary condition for other connected arc-transitive Cayley graphs on dihedral groups to be inner-automorphic. We further construct an infinite family of examples satisfying this condition, thereby demonstrating the existence of such graphs. Finally, we complete the classification of all 2-distance-transitive connected inner-automorphic Cayley graphs on dihedral groups. |
| title | On arc-transitive inner-automorphic Cayley graphs on dihedral groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2604.04366 |