Fault-Tolerant Hamiltonian Connectivity of Twisted Hypercube-Like Networks THLNs
Zhang Huifeng, Xirong Xu, Jing Guo, Yuansheng Yang · IEEE Access · 2018
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 Möbius cubes$MQ_{n}$.