Hamiltonian connectivity of restricted hypercube-like networks under the conditional fault model

Abstract

Restricted hypercube-like networks (RHLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, Möbius cubes, twisted cubes and locally twisted cubes. This paper deals with the fault-tolerant hamiltonian connectivity of RHLNs under the conditional fault model. Let $G$ be an $n$-dimensional RHLN and $F\subseteq V\left(G\right)\bigcup E\left(G\right)$, where $n\ge 7$ and $\mid F\mid \le 2n-10$. We prove that for any two nodes $u,v\in V(G-F)$ satisfying a simple necessary condition on neighbors of $u$ and $v$, there exists a hamiltonian or near-hamiltonian path between $u$ and $v$ in $G-F$. The result extends further the fault-tolerant graph embedding capability of RHLNs.