Fault-tolerant hamiltonian cycles and paths embedding into locally exchanged twisted cubes

The foundation of information society is computer interconnection network,and the key of information exchange is communication algorithm.Finding interconnection networks with simple routing algorithm and high fault-tolerant performance is the premise of realizing various communication algorithms and protocols.Nowadays,people can build complex interconnection networks by using very large scale integration(VLSI)technology.Locally exchanged twisted cubes,denoted by(s+t+1)-dimensional LeTQ_(s,t) which combines the merits of the exchanged hypercube and the locally twisted cube.It has been proved that the LeTQ_(s,t) has many excellent properties for interconnection networks,such as fewer edges,lower overhead and smaller diameter.Embeddability is an important indicator to measure the performance of interconnection networks.We mainly study the fault tolerant Hamiltonian properties of a faulty locally exchanged twisted cube,LeTQ_(s,t)-(f_(v)+f_(e)),with faulty vertices f_(v) and faulty edges fe.Firstly,we prove that an LeTQ_(s,t) can tolerate up to s-1 faulty vertices and edges when embedding a Hamiltonian cycle,for s≥2,t≥3,and s≤t.Furthermore,we also prove another result that there is a Hamiltonian path between any two distinct fault-free vertices in a faulty LeTQ_(s,t) with up to(s-2)faulty vertices and edges.That is,we show that LeTQ_(s,t) is(s-1)-Hamiltonian and(s-2)-Hamiltonian-connected.The results are proved to be optimal in this paper with at most(s-1)-fault-tolerant Hamiltonicity and(s-2)fault-tolerant Hamiltonian connectivity of LeTQ_(s,t).