Perfect codes in power graphs of finite groups

• Autorzy: Xuanlong Ma , Ruiqin Fu , Xuefei Lu , Mengxia Guo , Zhiqin Zhao
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Power graph; Enhanced power graph; Finite group; Perfect code; Total perfect code

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
• 94B99: None of the above, but in this section
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1440-1449

Daty

wydano

2017-01-01

otrzymano

2017-06-11

zaakceptowano

2017-09-21

online

2017-12-09

Twórcy

autor

Xuanlong Ma

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autor

Ruiqin Fu

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autor

Xuefei Lu

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autor

Mengxia Guo

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autor

Zhiqin Zhao

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Identyfikatory

DOI

10.1515/math-2017-0123