The power graph of a finite group
نویسندگان
چکیده
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 nonisomorphic 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.
منابع مشابه
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
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عنوان ژورنال:
- Discrete Mathematics
دوره 311 شماره
صفحات -
تاریخ انتشار 2011