Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Abstract

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