  Given a group $G$, let us connect two non-identity elements by an edge if and
only if one is a power of another. This gives a graph structure on $G$ minus
identity, called the reduced power graph. It is conjectured by Akbari and
Ashrafi that if a non-abelian finite simple group has a connected reduced power
graph, then it must be an alternating group.
  In this paper, we shall give a complete description of when the reduced power
graphs of $\mathrm{PGL}_n(\mathbb{F}_q)$ are connected for all $q$ and all
$n\geq 3$. In particular, the conjectured by Akbari and Ashrafi is false. We
shall also provide an upper bound in their diameters, and in case of
disconnection, provide a description of all connected components.
