Even cycles in enhanced hypercube networks under the conditional fault model

Let [Formula: see text] be an enhanced hypercube, which is an variant of the well-known hypercube [Formula: see text] and is constructed from [Formula: see text] by adding [Formula: see text] complementary edges. A network G is said to be under the conditional fault model if every fault-free vertex of G is incident to at least two fault-free edges. Let [Formula: see text] and [Formula: see text] be the set of faulty vertices and faulty edges in [Formula: see text], respectively. In this paper, under the conditional fault model, we prove that [Formula: see text] contains a fault-free cycle of every even length l with [Formula: see text] when [Formula: see text] and [Formula: see text].