Fault-tolerant cycles embedding in folded hypercubes

Abstract

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks (denoted by FQ n ) 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 FQ n has a cycle with length at least 2 n -2|F v | when the number of faulty vertices and non-critical edges is at most 2n - 4; where |F v | is the number of faulty vertices. It provides further theoretical evidence for the fact that FQ n has excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.