Fault-Tolerant Hamiltonian Connectivity of Twisted Hypercube-Like Networks THLNs

The twisted hypercube-like networks (THLNs) include some well-known hypercube variants. A graph G is k-fault-tolerant Hamiltonian connected if G - F remains Hamiltonian connected for every F subset of V(G) boolean OR E(G) with vertical bar F vertical bar <= k. This paper is concerned with the fault-tolerant Hamiltonian connectivity of an n-dimensional (n-D) THLN. Let G(n) be an n-D THLN (n >= 5) and F be a subset of V(G(n)) boolean OR E(G(n)) with vertical bar F vertical bar <= n - 2. We show that for arbitrary vertex-pair (u, v) in G(n) - F, there exists a (n - 2)-fault-tolerant Hamiltonian path joining vertices u and v except (u, v) being a weak vertex-pair in G(n) - F. The technical theorem proposed in this paper can be applied to several multiprocessor systems, including n-D crossed cubes CQ(n) n-D twisted cubes TQ(n) for odd n, n-D locally twisted cubes LTQ(n) and n-D Mobius cubes MQ(n).