Journal of Parallel and Distributed Computing ( IF 3.8 ) Pub Date : 2020-01-08 , DOI: 10.1016/j.jpdc.2019.12.009 Litao Guo , Chengfu Qin , Liqiong Xu
Hypercube and folded hypercube are the most fundamental interconnection networks for the attractive topological properties. We assume for any distinct vertices defined as local connectivity of and , is the maximum number of independent -paths in . Similarly, is local edge connectivity of . For some , and , if , then is -distance optimally (edge) connected, where is the diameter of and is the degree of . For all integers , if is -distance optimally connected, then we call is -distance local optimally connected. Similarly, we have the definition of -distance local optimally edge connected.
In this paper, we show that after deleting , and are 2-distance local optimally edge connected.
中文翻译:
距离最优边连接超立方体和折叠超立方体的子图容错
超立方和折叠式超立方是具有吸引人的拓扑特性的最基本的互连网络。我们假设有任何不同的顶点 定义为 和 ,是最大独立数 -路径 。同样, 是的本地边缘连接 。对于一些和 如果 , 然后 是 -最佳距离(边缘)连接,其中 是的直径 和 是的程度 。对于所有整数如果 是 -距离最佳连接,然后我们称 是 -距离本地最佳连接。同样,我们有以下定义-距离局部最佳边缘连接。
在本文中,我们表明删除后 , 和 是2距离局部最优边连接。