Reliability Evaluation of BC Networks

Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. Extra connectivity determination and faulty networks´ structure analysis are two important aspects for the reliability evaluation of interconnection networks. An n-dimensional bijective connection network (in brief, BC network), denoted by X_n, is an n-regular graph with 2ⁿ vertices and n2^n-1 edges. The hypercubes, Mobius cubes, crossed cubes, and twisted cubes are some examples of the BC networks. By exploring the boundary problem of the BC networks, we prove that when n ≥ 4 and 0 ≤ h ≤ n - 4 the h-extra connectivity of an n-dimensional BC network X_n is k_h(X_n = n(h + 1)- 1/2h (h + 3). Furthermore, there exists a large connected component and the remaining small components have at most h vertices in total if the total number of faulty vertices is strictly less its h-extra connectivity. As an application, the results on the h-extra connectivity and structure of faulty networks on hypercubes, Mobius cubes, crossed cubes, and twisted cubes are obtained.