Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups
A Cayley graph X = Cay(G, S) is called 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) =...
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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152186 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups / M. Ghasemi // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 52–58. — Бібліогр.: 14 назв. — англ. |
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irk-123456789-1521862019-06-09T01:24:56Z Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups Ghasemi, M. A Cayley graph X = Cay(G, S) is called 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| = 5n, and |Aut(X)| = 2m.3.5n, where m ∈ {2,3} and n ≥ 3, or Cay(G, S) where |G| = 5qn (q is prime) and |Aut(X)| = 2m.3.5.qn, where q ≥ 7, m ∈ {2,3} and n ≥ 1. 2012 Article Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups / M. Ghasemi // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 52–58. — Бібліогр.: 14 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:05C25, 20B25. http://dspace.nbuv.gov.ua/handle/123456789/152186 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A Cayley graph X = Cay(G, S) is called 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| = 5n, and |Aut(X)| = 2m.3.5n, where m ∈ {2,3} and n ≥ 3, or Cay(G, S) where |G| = 5qn (q is prime) and |Aut(X)| = 2m.3.5.qn, where q ≥ 7, m ∈ {2,3} and n ≥ 1. |
| format |
Article |
| author |
Ghasemi, M. |
| spellingShingle |
Ghasemi, M. Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups Algebra and Discrete Mathematics |
| author_facet |
Ghasemi, M. |
| author_sort |
Ghasemi, M. |
| title |
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_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_sort |
automorphism groups of tetravalent cayley graphs on minimal non-abelian groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152186 |
| citation_txt |
Automorphism groups of tetravalent Cayley graphs on minimal non-abelian groups / M. Ghasemi // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 52–58. — Бібліогр.: 14 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT ghasemim automorphismgroupsoftetravalentcayleygraphsonminimalnonabeliangroups |
| first_indexed |
2023-05-20T17:37:41Z |
| last_indexed |
2023-05-20T17:37:41Z |
| _version_ |
1796153723956756480 |