Automorphism groups of supergraphs of the power graph of a finite group

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• 作者：A. Hamzeh ^{hamze2006@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; A.R. Ashrafi
• 刊名：European Journal of Combinatorics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：Complete
• 页码：82-88
• 全文大小：377 K

文摘

For a finite group G$G$, the power graphP(G)$\mathcal{P}\left(G\right)$ is a graph with the vertex set G$G$, in which two distinct elements are adjacent if one is a power of the other. Feng, Ma and Wang (Feng et al., 2016) described the full automorphism group of P(G)$\mathcal{P}\left(G\right)$. In this paper, we study automorphism groups of the main supergraphs and cyclic graphs, which are supergraphs of P(G)$\mathcal{P}\left(G\right)$. It is proved that the automorphism group of these graphs can be written as a combination of Cartesian and wreath products of some symmetric groups. The full automorphism groups of these graphs of certain finite groups are also calculated.