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...
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| 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/1045 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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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