Let $G$ be an undirected graph. An $H$-structure-cut (resp. $H$-substructure-cut) of $G$ is a set of subgraphs of $G$, if any, whose deletion disconnects $G$, where the subgraphs deleted are isomorphic to a certain graph $H$ (resp. where for any $T^{\prime }$ of the subgraphs deleted, there is a subgraph $T$ of $G$, isomorphic to $H$, such that $T^{\prime }$ is a subgraph of $T$). $G$ is super$H{|}_M$-connected (resp. super sub-$H{|}_M$-connected) if the deletion of an arbitrary minimum $H$-structure-cut (resp. minimum $H$-substructure-cut) isolates a component isomorphic to a certain graph $M$. The $k$-ary $n$-cube $Q_n^k$ is one of the most attractive interconnection networks for multiprocessor systems. In this paper, we prove that $Q_n^k$ with $n\ge 3$ is super sub-$C_k{|}_{K_1}$-connected if $k\ge 3$ and $k$ is odd, and super $C_k{|}_{C_k}$-connected if $k\ge 5$ and $k$ is odd.

让 $G$是无向图。一个$H$-结构切割（resp。$H$-substructure-cut）$G$ 是一组子图 $G$，如果有的话，其删除将断开 $G$，其中删除的子图与某个图是同构的 $H$ （分别代表哪里 ${Ť}^{\prime }$ 在删除的子图中，有一个子图 $Ť$ 的 $G$，同构为 $H$，这样 ${Ť}^{\prime }$ 是的子图 $Ť$）。 $G$是超$H{|}_{\mathrm{中号}}$-已连接（分别是超级子-$H{|}_{\mathrm{中号}}$-connected），如果删除任意最小值$H$-结构切割（分别为最小值 $H$-substructure-cut）将同构的组件隔离到某个图 $\mathrm{中号}$。这$ķ$-ary $ñ$-立方体 ${问}_{ñ}^{ķ}$是多处理器系统最吸引人的互连网络之一。在本文中，我们证明${问}_{ñ}^{ķ}$ 和 $ñ\ge 3$ 是超级子$C_{ķ}{|}_{{ķ}_{\mathrm{1个}}}$-如果连接 $ķ\ge 3$ 和 $ķ$ 奇怪，超级 $C_{ķ}{|}_{C_{ķ}}$-如果连接 $ķ\ge 5$ 和 $ķ$ 很奇怪