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.