Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups
A Cayley graph \(X\)\(=\)Cay\((G,S)\) is called {\it normal} for \(G\) if the right regular representation \(R(G)\) of \(G\) is normal in the full automorphism group Aut\((X)\) of \(X\). In the present paper it is proved that all connected tetravalent Cayley graphs on a minimal non-abelian group \(...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/692 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543398340591616 |
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| author | Ghasemi, Mohsen |
| author_facet | Ghasemi, Mohsen |
| author_sort | Ghasemi, Mohsen |
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| collection | OJS |
| datestamp_date | 2018-04-04T09:42:12Z |
| description | A Cayley graph \(X\)\(=\)Cay\((G,S)\) is called {\it normal} for \(G\) if the right regular representation \(R(G)\) of \(G\) is normal in the full automorphism group Aut\((X)\) of \(X\). In the present paper it is proved that all connected tetravalent Cayley graphs on a minimal non-abelian group \(G\) are normal when \((|G|, 2)=(|G|,3)=1\), and \(X\) is not isomorphic to either Cay\((G,S)\), where \(|G|=5^n\), and \(|\)Aut(X)\(|\)\(=\)\(2^m.3.5^n\), where \(m \in \{2,3\}\) and \(n\geq 3\), or Cay\((G,S)\) where \(|G|=5q^n\) (\(q\) is prime) and \(|{\hbox{Aut}}(X)|=2^m.3.5.q^n\), where \(q\geq 7\), \(m \in \{2,3\}\) and \(n\geq 1\). |
| first_indexed | 2025-12-02T15:43:10Z |
| format | Article |
| id | admjournalluguniveduua-article-692 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:10Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6922018-04-04T09:42:12Z Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups Ghasemi, Mohsen Cayley graph, normal Cayley graph, minimal nonabelian group 05C25, 20B25 A Cayley graph \(X\)\(=\)Cay\((G,S)\) is called {\it normal} for \(G\) if the right regular representation \(R(G)\) of \(G\) is normal in the full automorphism group Aut\((X)\) of \(X\). In the present paper it is proved that all connected tetravalent Cayley graphs on a minimal non-abelian group \(G\) are normal when \((|G|, 2)=(|G|,3)=1\), and \(X\) is not isomorphic to either Cay\((G,S)\), where \(|G|=5^n\), and \(|\)Aut(X)\(|\)\(=\)\(2^m.3.5^n\), where \(m \in \{2,3\}\) and \(n\geq 3\), or Cay\((G,S)\) where \(|G|=5q^n\) (\(q\) is prime) and \(|{\hbox{Aut}}(X)|=2^m.3.5.q^n\), where \(q\geq 7\), \(m \in \{2,3\}\) and \(n\geq 1\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/692 Algebra and Discrete Mathematics; Vol 13, No 1 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/692/225 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Cayley graph normal Cayley graph minimal nonabelian group 05C25 20B25 Ghasemi, Mohsen Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title_full | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title_fullStr | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title_full_unstemmed | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title_short | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups |
| title_sort | automorphism groups of tetravalent cayley graphs on minimal non-abelian groups |
| topic | Cayley graph normal Cayley graph minimal nonabelian group 05C25 20B25 |
| topic_facet | Cayley graph normal Cayley graph minimal nonabelian group 05C25 20B25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/692 |
| work_keys_str_mv | AT ghasemimohsen automorphismgroupsoftetravalentcayleygraphsonminimalnonabeliangroups |