Cycles embedding on folded hypercubes with faulty nodes

Let FFvFFv be the set of faulty nodes in an nn-dimensional folded hypercube FQnFQn with |FFv|≤n−2|FFv|≤n−2. In this paper, we show that if n≥3n≥3, then every edge of FQn−FFvFQn−FFv lies on a fault-free cycle of every even length from 44 to 2n−2|FFv|2n−2|FFv|, and if n≥2n≥2 and nn is even, then every edge of FQn−FFvFQn−FFv lies on a fault-free cycle of every odd length from n+1n+1 to 2n−2|FFv|−12n−2|FFv|−1.