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 a cyclic group of order $n$ has oriented diameter $2$ for all $n\neq 2,4,6$. Until our work, to the best of our knowledge, no infinite family of graphs with oriented diameter 2 had been identified except for subclasses of complete graphs. Finally, we give a complete characterization of the oriented diameter of the power graphs of nilpotent groups. This, in turn, gives an algorithm for computing the oriented diameter of the power graph of a given nilpotent group that runs in time polynomial in the size of the group.