On conditional fault tolerance of hierarchical cubic networks

This paper considers the conditional fault tolerance, h-super connectivity kappa(h) and h-super edge-connectivity lambda(h) of the hierarchical cubic network HCNn, an attractive alternative network to the hypercube, and shows kappa(h)(HCNn) = lambda(h)(HCNn) = 2(h)(n + 1 - h) for any h with 0 <= h <= n - 1. The results imply that at least 2(h)(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. (C) 2018 Elsevier B.V. All rights reserved.