Edge-fault-tolerant hamiltonicity of locally twisted cubes under conditional edge faults

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 hamiltonicity of an n-dimensional locally twisted cube, denoted by LTQ (n) . We show that for any LTQ (n) (na parts per thousand yen3) 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.