Fault-tolerant Hamiltonicity of Dual-cube Extensive Networks

The hypercube family Qn is one of the most well-known interconnection networks in parallel computers. Using Qn, Li et al. introduced dualcube networks DC(n) and proved the vertex symmetry and some fault-tolerant hamiltonian properties of DC(n). Based on the structure of DC(n), Chen and Kao further introduced Dualcube Extensive Networks, denoted by DCEN(G). DCEN(G) is a wider family that contains DC(n) as a special case and preserves some nice properties of G such as the hamiltonian connectivity, globally 3*-connectivity, and edge-pancyclicity. In this article, we investigate the fault-tolerant hamiltonian property of DCEN(G). More specifically, let F ⊆ V (DCEN(G)) ∪ E(DCEN(G)) be the faulty set. We show that DCEN(G)−F contains a cycle that visits all vertices of DCEN(G) − F exactly once if G satisfies certain conditions.