The structure and metric dimension of the power graph of a finite group

The power graph PGPG of a finite group GG is the graph with the vertex set GG, where two distinct vertices are adjacent if one is a power of the other. We first show that PGPG has a transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups of GG (under usual inclusion) to characterize the structure of PGPG. Finally, a closed formula for the metric dimension of PGPG is established. As an application, we compute the metric dimension of the power graph of a cyclic group.