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Perfect codes in power graphs of finite groups

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Ma X., Fu R., Lu X., Guo M., Zhao Z.

Open Mathematics

2017

tom 15

nr 1

1440-1449

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.

Ograniczanie wyników

1 Open Mathematics

1 Fu R.

1 Guo M.

1 Lu X.

1 Ma X.

1 Zhao Z.

1 2017

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Perfect codes in power graphs of finite groups