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

The power graph P G of a finite group G is the graph with the vertex set G , where two distinct vertices are adjacent if one is a power of the other. We first show that P G 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 G (under usual inclusion) to characterize the structure of P G . Finally, a closed formula for the metric dimension of P G is established. As an application, we compute the metric dimension of the power graph of a cyclic group.