Fault-Tolerant Hamiltonicity of Twisted Cubes

The twisted cube TQn, is derived by changing some connection of hypercube Qn according to specific rules. Recently, many topological properties of this variation cube are studied. In this paper, we consider a faulty twisted n-cube with both edge and/or node faults. Let F be a subset of V(TQn)?E(TQn), we prove that TQn?F remains hamiltonian if |F|?n?2. Moreover, we prove that there exists a hamiltonian path in TQn?F joining any two vertices u, v in V(TQn)?F if |F|?n?3. The result is optimum in the sense that the fault-tolerant hamiltonicity (fault-tolerant hamiltonian connectivity respectively) of TQn is at most n?2 (n?3 respectively).

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