Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Let FvFv and FeFe be sets of faulty vertices and faulty edges, respectively, in the folded hypercube FQnFQn so that |Fv|+|Fe|≤n−2|Fv|+|Fe|≤n−2, for n≥2n≥2. Choose any fault-free edge e  . If n≥3n≥3 then there is a fault-free cycle of length l   in FQnFQn containing e, for every even l   ranging from 4 to 2n−2|Fv|2n−2|Fv|; if n≥2n≥2 is even then there is a fault-free cycle of length l   in FQnFQn containing e, for every odd l   ranging from n+1n+1 to 2n−2|Fv|−12n−2|Fv|−1.