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.

翻译：本文研究了群幂图的定向直径。我们证明了有限群的$2$-边连通幂图具有至多为$4$的定向直径。我们证明了对于所有$n\neq 2,4,6$，阶数为$n$的循环群的幂图具有定向直径$2$。据我们所知，在我们的工作之前，除了完全图的子类外，尚未发现具有定向直径$2$的无限图族。最后，我们完整刻画了幂零群幂图的定向直径。这进而给出了一种计算给定幂零群幂图定向直径的算法，该算法的运行时间关于群规模的规模为多项式级别。