## Abstract

The directed power graph of a group *G* is the digraph with vertex set *G*, having an arc from *y* to *x* whenever *x* is a power of *y*; the undirected power graph has an edge joining *x* and *y* whenever one is a power of the other. We show that, for a finite group, the undirected power graph determines the directed power graph up to isomorphism. As a consequence, two finite groups which have isomorphic undirected power graphs have the same number of elements of each order.

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