Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups
The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper we discuss the planarity and vertex connectivity of the power graphs of finite cyclic, dihedral and d...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153345 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups / S. Chattopadhyay, P. Panigrahi // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 42–49. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716494472806400 |
|---|---|
| author | Chattopadhyay, S. Panigrahi, P. |
| author_facet | Chattopadhyay, S. Panigrahi, P. |
| citation_txt | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups / S. Chattopadhyay, P. Panigrahi // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 42–49. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper we discuss the planarity and vertex connectivity of the power graphs of finite cyclic, dihedral and dicyclic groups. Also we apply connectivity concept to prove that the power graphs of both dihedral and dicyclic groups are not Hamiltonian.
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| first_indexed | 2025-12-07T18:05:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153345 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:05:38Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Chattopadhyay, S. Panigrahi, P. 2019-06-14T03:25:41Z 2019-06-14T03:25:41Z 2014 Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups / S. Chattopadhyay, P. Panigrahi // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 42–49. — Бібліогр.: 8 назв. — англ. 1726-3255 2010 MSC:05C25, 05C10, 05C40. https://nasplib.isofts.kiev.ua/handle/123456789/153345 The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper we discuss the planarity and vertex connectivity of the power graphs of finite cyclic, dihedral and dicyclic groups. Also we apply connectivity concept to prove that the power graphs of both dihedral and dicyclic groups are not Hamiltonian. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups Article published earlier |
| spellingShingle | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups Chattopadhyay, S. Panigrahi, P. |
| title | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| title_full | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| title_fullStr | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| title_full_unstemmed | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| title_short | Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| title_sort | connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153345 |
| work_keys_str_mv | AT chattopadhyays connectivityandplanarityofpowergraphsoffinitecyclicdihedralanddicyclicgroups AT panigrahip connectivityandplanarityofpowergraphsoffinitecyclicdihedralanddicyclicgroups |