Large scale multiprocessor systems or multicomputer systems, taking interconnection networks as underlying topologies, have been widely used in the big data era. Fault tolerance is becoming an essential attribute in multiprocessor systems as the number of processors is getting larger. A connected graph G is called strong Menger (edge) connected if, for any two distinct vertices u and v, there are min{dG(u),dG(v)} vertex (edge)-disjoint paths between them. Exchanged hypercube EH(s,t), as a variant of hypercube Qn, remains lots of preferable fault tolerant properties of hypercube. In this paper, we show that Qn − Qk (1 ≤ k ≤ n − 1) and EH(s,t) − Qk (2 ≤ k ≤min{s,t}) are strong Menger (edge) connected, respectively. Moreover, as a by-product, for dual cube Dn = EH(n − 1,n − 1), one popular generalization of hypercube, Dn − Qk is also showed to be strong Menger (edge) connected, where 1 ≤ k ≤ n − 1, n ≥ 3.

中文翻译：

---

超立方与交换超立方的基于子图的强门格尔连通性

以互连网络为底层拓扑的大规模多处理器系统或多计算机系统在大数据时代得到了广泛的应用。随着处理器数量的增加，容错正在成为多处理器系统中的一个基本属性。连通图G被称为强门格尔（边）连接如果，对于任何两个不同的顶点你和v， 有分钟{dG(你),dG(v)}顶点（边）——它们之间的不相交路径。交换超立方体乙H(s,吨)，作为超立方体的变体问n，仍然保留了超立方体的许多可取的容错特性。在本文中，我们表明问n - 问ķ (1 ≤ ķ ≤ n - 1)和乙H(s,吨) - 问ķ (2 ≤ ķ ≤分钟{s,吨})分别是强门格尔（边）连通的。此外，作为副产品，对于双立方体Dn = 乙H(n - 1,n - 1)，超立方体的一种流行推广，Dn - 问ķ也被证明是强门格尔（边）连通的，其中1 ≤ ķ ≤ n - 1, n ≥ 3.