Fault-Tolerant Pancyclicity of the Möbius Cubes

The Möbius cube MQn proposed by Cull et al. is an alternative to the popular hypercube network. Recently, MQn was shown to be pancyclic, i.e., cycles of any lengths at least four can be embedded into it. Due to the importance of the fault tolerance in the parallel processing area, in this paper, we study an injured MQn with mixed node and link faults. We show that it is (n − 2)-fault-tolerant pancyclic for n ≥ 3, that is, an injured n-dimensional MQn is still pancyclic with up to (n−2) faults. Furthermore, our result is optimal. key words: cycle embedding, Möbius cube, pancyclic, hamiltonian, fault tolerance