The power graph \({\mathcal {P}}_{G}\) of a finite group G is the graph whose vertex set is G, two distinct vertices are adjacent if one is a power of the other. The order supergraph \({\mathcal {S}}_{G}\) of \({\mathcal {P}}_G\) is the graph with vertex set G, and two distinct vertices x, y are adjacent if o(x)|o(y) or o(y)|o(x). In this paper, we study the independence number of \({\mathcal {S}}_{G}\) and answer a question was posed by Hamzeh and Ashrafi.

中文翻译：

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关于有限群的幂图的阶主管

有限群G的幂图\（{\数学{P}} _ {G} \）是顶点集为G的图，如果一个是另一个的幂，则两个不同的顶点相邻。顺序母图\（{\ mathcal {S}} _ {G} \）的\（{\ mathcal {P}} _ G ^ \）是与顶点集合的曲线G ^，和两个不同的顶点X，  ÿ相邻当ö（x）| o（y）或o（y）| o（x）。在本文中，我们研究\（{\ mathcal {S}} _ {G} \）的独立数 并回答了哈姆齐和阿什拉菲的问题。