Reliability Assessment of Hierarchical Hypercube Networks

The g-good neighbor connectivity κ g (G) and g-good-neighbor diagnosability t g (G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G.So far, almost all known results about κ g (G) and t g (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 κ g (HHC n ) and t g (HHC n ) for the n-dimensional hierarchical hypercube network HHC n for 1 ≤ g ≤ m -1 and m ≥ 2, where n = 2 m + m.We show that κ g (HHC n ) = 2 g (m + 1 -g) for 1 ≤ g ≤ m -1.In addition, we show that t g (HHC n ) = 2 g (m + 2 -g) -1 under the PMC model and MM * model for 1 ≤ g ≤ m -1.