| Autor: |
Ma Xuanlong, Fu Ruiqin, Lu Xuefei, Guo Mengxia, Zhao Zhiqin |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
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| Zdroj: |
Open Mathematics, Vol 15, Iss 1, Pp 1440-1449 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
2391-5455 |
| DOI: |
10.1515/math-2017-0123 |
| Popis: |
The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the group, in which two vertices are adjacent if they generate a cyclic subgroup. In this paper, we give a complete description of finite groups with enhanced power graphs admitting a perfect code. In addition, we describe all groups in the following two classes of finite groups: the class of groups with power graphs admitting a total perfect code, and the class of groups with enhanced power graphs admitting a total perfect code. Furthermore, we characterize several families of finite groups with power graphs admitting a perfect code, and several other families of finite groups with power graphs which do not admit perfect codes. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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