Let [Formula: see text] be an undirected graph. An [Formula: see text]-structure-cut (resp. [Formula: see text]-substructure-cut) of [Formula: see text] is a set of subgraphs of [Formula: see text], if any, whose deletion disconnects [Formula: see text], where the subgraphs deleted are isomorphic to a certain graph [Formula: see text] (resp. where for any [Formula: see text] of the subgraphs deleted, there is a subgraph [Formula: see text] of [Formula: see text], isomorphic to [Formula: see text], such that [Formula: see text] is a subgraph of [Formula: see text]). [Formula: see text] is super[Formula: see text]-connected (resp. super sub-[Formula: see text]-connected) if the deletion of an arbitrary minimum [Formula: see text]-structure-cut (resp. minimum [Formula: see text]-substructure-cut) isolates a component isomorphic to a certain graph [Formula: see text]. The [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] is one of the most attractive interconnection networks for multiprocessor systems. In this paper, we prove that [Formula: see text] with [Formula: see text] is super sub-[Formula: see text]-connected if [Formula: see text] and [Formula: see text] is odd, and super [Formula: see text]-connected if [Formula: see text] and [Formula: see text] is odd.

中文翻译：

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k-Ary n-Cube 网络的 Super Ck 和 Sub-Ck 连通性

令 [公式：见正文] 为无向图。[Formula: see text] 的 [Formula: see text]-structure-cut (resp. [Formula: see text]-substructure-cut) 是 [Formula: see text] 的一组子图，如果有的话，其删除断开[公式：见文本]，其中删除的子图同构于某个图[公式：见文本]（分别对于删除的子图的任何[公式：见文本]，有一个子图[公式：见文本] 的 [Formula: see text]，同构到 [Formula: see text]，使得 [Formula: see text] 是 [Formula: see text] 的子图）。[公式：见正文]是超[公式：见正文]-connected(resp. super sub-[公式：见正文]-connected)如果删除任意最小值[公式：见正文]-structure-cut(resp. . 最小 [公式：见文本]-substructure-cut) 分离出同构于某个图的组件 [公式：见文本]。[公式：见正文]-ary [公式：见正文]-cube [公式：见正文]是多处理器系统最有吸引力的互连网络之一。在本文中，我们证明如果[公式：参见文本]和[公式：参见文本]是奇数，则[公式：参见文本]和[公式：参见文本]是超子[公式：参见文本]-连通的，并且super [Formula: see text] - 如果 [Formula: see text] 和 [Formula: see text] 是奇数，则连接。