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Displaying similar documents to “Perfect codes in regular graphs”

Perfect codes in power graphs of finite groups

Xuanlong Ma, Ruiqin Fu, Xuefei Lu, Mengxia Guo, Zhiqin Zhao (2017)

Open Mathematics

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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...