The solubility graph associated with a finite group [Formula: see text] is a simple graph whose vertices are the elements of [Formula: see text], and there is an edge between two distinct elements [Formula: see text] and [Formula: see text] if and only if [Formula: see text] is a soluble subgroup of [Formula: see text]. We examine some properties of solubility graphs.

中文翻译：

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与有限群相关的溶解度图

与有限群相关的溶解度图 [公式：见正文] 是一个简单的图，其顶点是 [公式：见正文] 的元素，两个不同的元素 [公式：见正文] 和 [公式： see text] 当且仅当 [Formula: see text] 是 [Formula: see text] 的可溶子群。我们检查溶解度图的一些性质。