The power graph of a finite group
The power graph of a finite group
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DOI：
10.1016/j.disc.2010.02.011
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发表时间：
2011-07-06
影响因子：
0.8
通讯作者：
Ghosh, Shamik
中科院分区：
文献类型：
--
作者：
Cameron, Peter J.;Ghosh, Shamik
群的幂图是其顶点集是群的图，如果一个元素是另一个元素的幂，则两个元素相邻。我们观察到，非同构的有限群可以有同构的幂图，但有限阿贝尔群同构的幂图必须是同构的。我们猜想两个具有同构幂图的有限群的每阶元素个数相等。我们还证明了唯一自同构群与其幂图的自同构群相同的有限群是4阶克莱因群。(C)2010 Elsevier B.V.保留所有权利。
The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that non-isomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs have the same number of elements of each order. We also show that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4. (C) 2010 Elsevier B.V. All rights reserved.