On conditional fault tolerance of hierarchical cubic networks

This paper considers the conditional fault tolerance, h-super connectivity κ and h-super edge-connectivity λ of the hierarchical cubic network HCNn, an attractive alternative network to the hypercube, and shows κ(HCNn) = λ (HCNn) = 2 (n+ 1− h) for any h with 0 ≤ h ≤ n− 1. The results imply that at least 2(n+ 1− h) vertices or edges have to be removed from HCNn to make it disconnected with no vertices of degree less than h, and generalize some known results.