On Oriented Diameter of Power Graphs

In this paper, we study the oriented diameter of power graphs of groups. We show that a 2-edge connected power graph of a finite group has oriented diameter at most 4. We prove that the power graph of the cyclic group of order n has oriented diameter 2 for all n≠1,2,4,6. We show that the oriented diameter of 2-edge connected power graphs of non-cyclic nilpotent groups is either 3 or 4. Moreover, we provide necessary and sufficient conditions to determine when such graphs have oriented diameter 3 and when these graphs have diameter 4. This, in turn, gives a polynomial time algorithm for computing the oriented diameter of the power graph of a given nilpotent group.