Fault-Tolerant Ring Embedding in Star Graphs

In this paper, we consider an injured star graph with some faulty links and nodes. We show that even with fe n 3 faulty links a Hamiltonian cycle still can be found in an nstar, and that with fv n 3 faulty nodes a ring containing at most 4fv nodes less than that in a Hamiltonian cycle can be found (i.e., containing at leastn! 4fv nodes). In general, in an n-star with fe faulty links and fv faulty nodes, where fe + fv n 3, our embedding is able to establish a ring containing at least n! 4fv nodes.