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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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1045 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10452018-04-26T02:28:53Z Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups Chattopadhyay, Sriparna Panigrahi, Pratima power graph, connectivity, planarity, cyclic group, dihedral group, dicyclic group 05C25, 05C10, 05C40 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1045 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1045/567 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
power graph connectivity planarity cyclic group dihedral group dicyclic group 05C25 05C10 05C40 |
| spellingShingle |
power graph connectivity planarity cyclic group dihedral group dicyclic group 05C25 05C10 05C40 Chattopadhyay, Sriparna Panigrahi, Pratima Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| topic_facet |
power graph connectivity planarity cyclic group dihedral group dicyclic group 05C25 05C10 05C40 |
| format |
Article |
| author |
Chattopadhyay, Sriparna Panigrahi, Pratima |
| author_facet |
Chattopadhyay, Sriparna Panigrahi, Pratima |
| author_sort |
Chattopadhyay, Sriparna |
| title |
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_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_sort |
connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1045 |
| work_keys_str_mv |
AT chattopadhyaysriparna connectivityandplanarityofpowergraphsoffinitecyclicdihedralanddicyclicgroups AT panigrahipratima connectivityandplanarityofpowergraphsoffinitecyclicdihedralanddicyclicgroups |
| first_indexed |
2024-04-12T06:25:58Z |
| last_indexed |
2024-04-12T06:25:58Z |
| _version_ |
1796109142574759936 |