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 $F\subset V(G)\cup E(G)$ with $|F|\leq k$ . 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 ( $n\geq 5$ ) and $F$ be a subset of $V(G_{n})\cup E(G_{n})$ with $|F|\leq n-2$ . 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 $MQ_{n}$ .