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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/692 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \(n\geq 1\). |
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