We study group power digraphs
,
where
is a finite
group and
is a positive integer. A group power digraph is a directed graph derived from the power
function
on a
finite group
.
We present results on various properties of these power digraphs, including indegree
of vertices, structure of components, existence of cycles, and a certain type of
symmetry. Arbitrary finite groups are discussed briefly, but the focus of this paper is
on three families of finite groups: cyclic, dihedral, and symmetric groups. In each
case, properties specific to the family of groups are presented.
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