Automorphism groups of supergraphs of the power graph of a finite group
Automorphism groups of supergraphs of the power graph of a finite group
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DOI：
10.1016/j.ejc.2016.09.005
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发表时间：
2017-02
期刊：
影响因子：
--
通讯作者：
A. Hamzeh;A. Ashrafi
中科院分区：
文献类型：
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作者：
A. Hamzeh;A. Ashrafi
对于有限群G，幂图P（G）是顶点集为G的图，其中两个不同的元素相邻，如果一个是另一个的幂。Feng，Ma和Wang（Feng等人，2016）描述了P（G）的全自同构群。本文研究了P（G）的主超图和循环图的自同构群。证明了这些图的自同构群可以表示为某些对称群的笛卡尔积和圈积的组合。计算了某些有限群的图的全自同构群。
For a finite group G, the power graph P (G) is a graph with the vertex set 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). In this paper, we study automorphism groups of the main supergraphs and cyclic graphs, which are supergraphs of P (G). 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.