Fault-Free Hamiltonian Cycles in Locally Twisted Cubes under Conditional Edge Faults

摘要

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 LTQ{sub}n. We show that for any LTQ{sub}n (n ≥ 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.