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

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 GG be an nn-dimensional RHLN and F⊆V(G)⋃E(G)F⊆V(G)⋃E(G), where n≥7n≥7 and ∣F∣≤2n−10∣F∣≤2n−10. We prove that for any two nodes u,v∈V(G−F)u,v∈V(G−F) satisfying a simple necessary condition on neighbors of uu and vv, there exists a hamiltonian or near-hamiltonian path between uu and vv in G−FG−F. The result extends further the fault-tolerant graph embedding capability of RHLNs.

► Twisted hypercube-like networks are an important class of generalizations of most well-known variants of the hypercube.
► There exists a fault-tolerant hamiltonian or near-hamiltonian path in THLNs with up to 2n−102n−10 faulty elements.
► THLNs exhibit excellent fault-tolerant graph embedding capability.