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，如果对每个图 $G\in\mathcal{C}$ 和每个 $k\in\mathbb{N}$，有 $G^k\in\mathcal{C}$。若对每个 $k\in\mathbb{N}$，只要 $G^k\in\mathcal{C}$，就有 $G^{k+1}\in\mathcal{C}$，则 $\mathcal{C}$ 在幂运算下强封闭。已知圆弧图和真圆弧图在幂运算下封闭，但这些图类是否也在幂运算下强封闭仍是开放问题。本文解决了这些问题。