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 Q n , k (one potential alternative of hypercube) for 1 ≤ h ≤ 2 ⌈ n 2 ⌉ + 1 , n ≥ 2 k + 4 and 1 ≤ h ≤ 2 ⌈ n 2 ⌉ , n ≤ 2 k + 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 Q n , k for 1 ≤ g ≤ 2 ⌈ n 2 ⌉ + 1 , n ≥ 13 . As an easy extension, similar results for folded hypercube F Q n , another popular network structure, are readily derived.

中文翻译：

---

基于增强超立方体的多处理器系统可靠性测度

摘要 多处理器系统的可靠性度量对于多处理器系统的设计和维护具有重要意义。基于边缘连通性，引入了更精细的多处理器系统可靠性量化指标。额外的边缘连接和组件边缘连接作为评估多处理器系统鲁棒性的两个重要参数，被广泛探索。在本文中，我们首先确定了增强型超立方体 Q n , k（超立方体的一种潜在替代方案）的 h -extra 边缘连通性对于 1 ≤ h ≤ 2 ⌈ n 2 ⌉ + 1 ，n ≥ 2 k + 4 和 1 ≤ h ≤ 2 ⌈ n 2 ⌉ , n ≤ 2 k + 3 , k ≥ 3 。Zhang 等人 先前的一些结果。(2016) 和 Sabir 等人。(2019) 延长。而且，我们还建立了 n 维增强超立方体 Q n 的 g 分量边缘连通性，k 为 1 ≤ g ≤ 2 ⌈ n 2 ⌉ + 1 ，n ≥ 13 。作为一个简单的扩展，折叠超立方体 FQ n（另一种流行的网络结构）的类似结果很容易推导出来。