On Cayley representations of central Cayley graphs over almost simple groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916276076544000 |
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| author | Guo, Jin Guo, Wenbin Ryabov, Grigory Vasil'ev, Andrey V. |
| author_facet | Guo, Jin Guo, Wenbin Ryabov, Grigory Vasil'ev, Andrey V. |
| contents | A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$. We prove that every central Cayley graph over a simple group $G$ has at most two pairwise nonequivalent Cayley representations over $G$ associated with the subgroups of $Sym(G)$ induced by left and right multiplications of $G$. We also provide an algorithm which, given a central Cayley graph $Γ$ over an almost simple group $G$ whose socle is of a bounded index, finds the full set of pairwise nonequivalent Cayley representations of $Γ$ over $G$ in time polynomial in size of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_05838 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Cayley representations of central Cayley graphs over almost simple groups Guo, Jin Guo, Wenbin Ryabov, Grigory Vasil'ev, Andrey V. Group Theory Combinatorics 05C60, 05E18, 20B35, 20D06 A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$. We prove that every central Cayley graph over a simple group $G$ has at most two pairwise nonequivalent Cayley representations over $G$ associated with the subgroups of $Sym(G)$ induced by left and right multiplications of $G$. We also provide an algorithm which, given a central Cayley graph $Γ$ over an almost simple group $G$ whose socle is of a bounded index, finds the full set of pairwise nonequivalent Cayley representations of $Γ$ over $G$ in time polynomial in size of $G$. |
| title | On Cayley representations of central Cayley graphs over almost simple groups |
| topic | Group Theory Combinatorics 05C60, 05E18, 20B35, 20D06 |
| url | https://arxiv.org/abs/2112.05838 |