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 connected if and only if they invariably generate $G$. In this paper we study this object for alternating and symmetric groups. First we observe that in most cases it has isolated vertices. Then, we prove that if we take them out we obtain a connected graph. Finally, we bound the diameter of this new graph from above and from below --- apart from trivial cases, it is between $3$ and $6$ ---, and in about half of the cases we compute it exactly. 查看全文>>