A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular arc graphs and proper circular arc graphs are closed under powers. But it is open whether these classes of graphs are also strongly closed under powers. In this paper we have settled these problems.

翻译：图类$\mathcal{C}$在幂运算下封闭，若对任意图$G\in\mathcal{C}$及任意$k\in\mathbb{N}$，有$G^k\in\mathcal{C}$。此外，$\mathcal{C}$在幂运算下强封闭，若对任意$k\in\mathbb{N}$，当$G^k\in\mathcal{C}$时，则$G^{k+1}\in\mathcal{C}$。已知圆弧图及真圆弧图均在幂运算下封闭。但这两类图是否也在幂运算下强封闭尚属开放问题。本文解决了这些问题。