Hamiltonian Cycle in Folded Hypercubes With Highly Conditional Edge Faults
Che-Nan Kuo, Yu‐Huei Cheng · IEEE Access · 2020
As an extension of the n-dimensional hypercube Qn, the n-dimensional folded hypercube denoted as FQn, which can be structured from Qnadding an edge to every pair of vertices with complementary addresses.FQnpossesses many properties superior to those of Qn, such as diameter, fault diameter, connectivity, and so on. In this paper, let FFedenote the set of faulty edges in FQnand assume that each vertex is incident to at least three fault-free edges in FQn- FFe. Then, we show that FQn- FFecontains a fault-free Hamiltonian cycle of length 2n, where n ≥ 3 and |FFe| ≤ 3n - 7.