Hamiltonian Cycle in Folded Hypercubes With Highly Conditional Edge Faults

As an extension of the n-dimensional hypercube Q
_n
, the n-dimensional folded hypercube denoted as FQ
_n
, which can be structured from Q
_n
adding an edge to every pair of vertices with complementary addresses.FQ
_n
possesses many properties superior to those of Q
_n
, such as diameter, fault diameter, connectivity, and so on. In this paper, let FF
_e
denote the set of faulty edges in FQ
_n
and assume that each vertex is incident to at least three fault-free edges in FQ
_n
- FF
_e
. Then, we show that FQ
_n
- FF
_e
contains a fault-free Hamiltonian cycle of length 2
ⁿ
, where n ≥ 3 and |FF
_e
| ≤ 3n - 7.