Fault-Tolerant Cycles Embedding in Folded Hypercubes

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks(denoted by FQ) acts as the host graph, and the longest fault-free cycle represents the guest graph. Under the conditions looser than that of previous works, it is shown that FQhas a cycle with length at least 2~n-2︱F︱ when the number of faulty vertices and non-critical edges is at most 2n-4; where ︱F︱ is the number of faulty vertices. It provides further theoretical evidence for the fact that FQhas excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.