Graphical regular representations of $(2,p)$-generated groups
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929474972418048 |
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| author | Xia, Binzhou |
| author_facet | Xia, Binzhou |
| contents | For groups $G$ that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of $G$ to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to $G$. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, $k$-valent GRRs of finite nonabelian simple groups with $k\geq5$ are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graphical regular representations of $(2,p)$-generated groups Xia, Binzhou Group Theory Combinatorics For groups $G$ that can be generated by an involution and an element of odd prime order, this paper gives a sufficient condition for a certain Cayley graph of $G$ to be a graphical regular representation (GRR), that is, for the Cayley graph to have full automorphism group isomorphic to $G$. This condition enables one to show the existence of GRRs of prescribed valency for a large class of groups, and in this paper, $k$-valent GRRs of finite nonabelian simple groups with $k\geq5$ are considered. |
| title | Graphical regular representations of $(2,p)$-generated groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2304.00541 |