STRUCTURES OF POWER DIGRAPHSASSOCIATED WITHxpk≡y(modn)WHEREpIS AN ODD PRIME

Abstract

Let
k
and
n
be positive integers and
p
be an odd prime. A power
digraph
G
(
p
k
, n
) for which the vertex set is
{
0
,
1
,
2
, . . . , n
−
1
}
and (
u, v
)
is a directed edge from a vertex
u
to a vertex
v
if
u
p
k
≡
v
(mod
n
). We
study the structures of this power digraphs. Moreover, we provide some
interesting results when
p
is 3
,
5 or 7.