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：$\ mathcal{ C} $\ mathcal{ C} $ 在权力下关闭, 如果每张图形$G\ intcal{ C} $和每张 $k\ in\ mathbb{ N} $, $G\ k\ in\ mathcal{ C} $ 和每张 $k\ in\ mathbb{ N} $, 美元和每张 mathb{ N} $, 美元和每张 mathb{ N} $, 美元和每张 $k\ k\ in\ mathcal{ C} $, 美元和每张图表在权力下关闭, 美元和 macrcrc} 美元。 如果每张图表在权力下也严格关闭, 美元 $k\ k\ mathb{ C} $, 美元在权力下关闭, 美元 美元和 美元 美元, 美元 则某几张图表 在本文中我们解决了这些问题 。
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