Fault-free cycles embedding in folded hypercubes with F4

Abstract

The n-dimensional folded hypercube FQn interconnection network has been shown that it is bipartite for every odd n≥3, and which is non-bipartite for every even n≥2. Let F4={f1,f2,f3,f4} denote the faulty set of extreme vertices from any four cycle in FQn. Then, we show that the fault-free cycles can be embedded in FQn−F4 as follows:1.For n≥3, FQn−F4 contains a fault-free cycle of every even length from 4 to 2n−4;2.For every even n≥4, FQn−F4 contains a fault-free cycle of every odd length from n+1 to 2n−5.The results are optimal with respect to the length type of embedded cycles in FQn−F4.