The connectivity of edge-fault-tolerant enhanced hypercube

Duo to its topological advantages, the enhanced hypercube network Q_n,k (n, k are positive integers, 1 ≤ k ≤ n - 1) is one of the most versatile and efficient interconnection networks (networks for short) so far discovered for parallel computation. To fully realize its potential in those networks where reliability and speed are critical, the topological properties of the enhanced hypercube network need to be further discovered. In this paper, the topological structure of n-dimensional enhanced hypercube Q_n,k is analyzed. Consequently, the properties related to hamiltonian connectivity in faulty Q_n,k have been investigated. Let F denote the set of fault edges. Tt has been found that when |F| ≤ n - 1, if n and k have the same parity, then for any two different vertices x, y ∈ Q_n,k - F (x and y are in the same partite set), there exists a path of length 2ⁿ - 2 from x and y.