Fault-free Hamiltonian cycles in locally twisted cubes under conditional edge faults

Abstract

The locally twisted cube is a variation of hypercube, which possesses some properties superior to the hypercube. In this paper, we investigate the edge-fault-tolerant Hamiltoncity of an n-dimensional locally twisted cube, denoted by LTQn. We show that for any LTQn (n ges 3) with at most 2n - 5 faulty edges in which each node is incident to at least two fault-free edges, there exists a fault-free Hamiltonian cycle. We also demonstrate that our result is optimal with respect to the number of faulty edges tolerated.