Fault-tolerant pancyclicity of the Mobius cubes

Abstract

The Mobius cube MQ(n) proposed by Cull et al. is an alternative to the popular hypercube network. Recently, MQ(n) 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 MQ(n) with mixed node and link faults. We show that it is (n - 2)-fault-tolerant pancyclic for n greater than or equal to 3, that is, an injured n-dimensional MQ(n) is still pancyclic with up to (n - 2) faults. Furthermore, our result is optimal.