Reliability Assessment of Hierarchical Hypercube Networks
Shu-Li Zhao, Rong‐Xia Hao · IEEE Access · 2019
The g-good neighbor connectivity κg(G) and g-good-neighbor diagnosability tg(G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G. So far, almost all known results about κg(G) and tg(G) are about special g except the hypercubes, the star graphs, the k-ary n-cubes, and so on. In this paper, we focus on κg(HHCn) and tg(HHCn) for the n-dimensional hierarchical hypercube network HHCnfor 1 ≤ g ≤ m - 1 and m ≥ 2, where n = 2m+ m. We show that κg(HHCn) = 2g(m + 1 - g) for 1 ≤ g ≤ m - 1. In addition, we show that tg(HHCn) = 2g(m + 2 - g) - 1 under the PMC model and MM* model for 1 ≤ g ≤ m - 1.