Issue No. 11 - Nov. (2013 vol. 62)

ISSN: 0018-9340

pp: 2337-2340

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2012.106

Qiang Zhu , Xidian University, Xi'an

Xin-Ke Wang , Xidian University, Xi'an

Guanglan Cheng , Xidian University, Xi'an

ABSTRACT

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 $(2^{n})$ vertices and $(n2^{n-1})$ edges. The hypercubes, M$(\ddot{o})$bius 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 $(n\ge 4)$ and $(0\le h\le n-4)$ the $(h)$-extra connectivity of an $(n)$-dimensional BC network $(X_n)$ is $(\kappa_{h}(X_n)=)$ $(n(h+1)-{1\over 2} h(h+3))$. 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, M$(\ddot{o})$bius cubes, crossed cubes, and twisted cubes are obtained.

INDEX TERMS

Hypercubes, Multiprocessing systems, Computer network reliability, Program processors, Software reliability,interconnection networks, BC networks, reliability, maximally connected component, extra connectivity

CITATION

Qiang Zhu, Xin-Ke Wang, Guanglan Cheng, "Reliability Evaluation of BC Networks",

*IEEE Transactions on Computers*, vol. 62, no. , pp. 2337-2340, Nov. 2013, doi:10.1109/TC.2012.106