On Hamiltonian properties of unidirectional hypercubes
In this paper, we study the arc fault-tolerance Hamiltonian properties for unidirectional hypercube UQn U Q n . Let F  be a set of arcs in UQn U Q n . We show that UQn?F U Q n ? F is Hamiltonian if | F | ? ? n 2 ? ? 1 . We present the necessary and sufficient condition for vertices u and v  in UQn U Q n such that there exists a Hamiltonian path P(u,v) P ( u , v ) . We prove that there exists a Hamiltonian path P(u,v) P ( u , v ) in UQn?F U Q n ? F for | F | ? ? n 2 ? ? 2 and u,v u , v satisfying the necessary condition. The numbers of faulty arcs for these results are optimal.
unidirectional hypercubes interconnection networks fault hamiltonicity