Given a connected graph G and $S\subseteq V(G)$ with $|S|\ge 2$, a tree T in G is called an S-Steiner tree (or S-tree for short) if $S\subseteq V(T)$. Two S-trees $T_1$ and $T_2$ are internally disjoint if $E(T_1)\cap E(T_2)=\varnothing$ and $V(T_1)\cap V(T_2)=S$. The packing number of internally disjoint S-trees, denoted as ${\kappa }_G(S)$, is the maximum size of a set of internally disjoint S-trees in G. For an integer $k\ge 2$, the generalized k-connectivity (abbr. ${\kappa }_k$-connectivity) of a graph G is defined as ${\kappa }_k(G)=\text{min}\{{\kappa }_G(S)|S\subseteq V(G)$ and $|S|=k\}$. The n-dimensional augmented cube, denoted as $A{Q}_n$, is an important variant of the hypercube that possesses several desired topology properties such as diverse embedding schemes in applications of parallel computing. In this paper, we focus on the study of constructing internally disjoint S-trees with $|S|=3$ in $A{Q}_n$. As a result, we completely determine the ${\kappa }_3$-connectivity of $A{Q}_n$ as follows: ${\kappa }_3(A{Q}_4)=5$ and ${\kappa }_3(A{Q}_n)=2n-2$ for $n=3$ or $n\ge 5$.

给定一个连通图G和$\mathrm{小号}\subseteq \mathrm{伏特}（G）$ 和 $|\mathrm{小号}|\ge \mathrm{2个}$，树Ť在ģ称为小号-Steiner树（或小号-tree的简称）如果$\mathrm{小号}\subseteq \mathrm{伏特}（Ť）$。两个小号-树${Ť}_{\mathrm{1个}}$ 和 ${Ť}_{\mathrm{2个}}$ 在内部不相交，如果 $E（{Ť}_{\mathrm{1个}}）\cap E（{Ť}_{\mathrm{2个}}）=\varnothing$ 和 $\mathrm{伏特}（{Ť}_{\mathrm{1个}}）\cap \mathrm{伏特}（{Ť}_{\mathrm{2个}}）=\mathrm{小号}$。内部不相交的S树的包装数，表示为${\kappa }_G（\mathrm{小号}）$是G中一组内部不相交S树的最大大小。对于整数$ķ\ge \mathrm{2个}$，广义k连通性（缩写${\kappa }_{ķ}$图G的-连通性定义为${\kappa }_{ķ}（G）=\text{分}\{{\kappa }_G（\mathrm{小号}）|\mathrm{小号}\subseteq \mathrm{伏特}（G）$ 和 $|\mathrm{小号}|=ķ\}$。在ñ维增强立方体，表示为$\mathrm{一种}{问}_{ñ}$是超多维数据集的重要变体，它具有几个所需的拓扑属性，例如并行计算应用程序中的各种嵌入方案。在本文中，我们专注于构造内部不相交的S-树的研究。$|\mathrm{小号}|=3$ 在 $\mathrm{一种}{问}_{ñ}$。结果，我们完全确定了${\kappa }_3$的连接性 $\mathrm{一种}{问}_{ñ}$ 如下： ${\kappa }_3（\mathrm{一种}{问}_4）=5$ 和 ${\kappa }_3（\mathrm{一种}{问}_{ñ}）=\mathrm{2个}ñ-\mathrm{2个}$ 为了 $ñ=3$ 或者 $ñ\ge 5$。