Reliability measure of multiprocessor system based on enhanced hypercubes

Abstract

Reliability measure of multiprocessor systems is of significant importance to the design and maintenance of multiprocessor systems. Based on edge connectivity, more refined quantitative indicators for the reliability of multiprocessor systems have been introduced. The extra edge connectivity and the component edge connectivity, as two important parameters to evaluate the robustness of multiprocessor systems, are explored extensively. In this paper, we first determine the h-extra edge connectivity of the enhanced hypercube Qn,k (one potential alternative of hypercube) for 1≤h≤2⌈n2⌉+1, n≥2k+4 and 1≤h≤2⌈n2⌉, n≤2k+3, k≥3. Some previous results in Zhang et al. (2016) and Sabir et al. (2019) are extended. Moreover, we also establish the g-component edge connectivity of the n-dimensional enhanced hypercube Qn,k for 1≤g≤2⌈n2⌉+1, n≥13. As an easy extension, similar results for folded hypercube FQn, another popular network structure, are readily derived.