Abstract Given a finite group G, the invariably generating graph of G is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of G, and two classes are adjacent if and only if they invariably generate G. In this paper, we study this object for alternating and symmetric groups. The main result of the paper states that if we remove the isolated vertices from the graph, the resulting graph is connected and has diameter at most 6.

中文翻译：

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交替对称群的不变生成图

摘要 给定一个有限群 G，G 的不变生成图定义为无向图，其中顶点是 G 的非平凡共轭类，并且两个类相邻当且仅当它们总是生成 G。在本文中，我们研究这个对象的交替和对称群。论文的主要结果表明，如果我们从图中删除孤立的顶点，则生成的图是连通的，并且直径最多为 6。