Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures

The star graph interconnection network has been recognized as an attractive alternative to the hypercube network. Previously, the star graph has been shown to contain a Hamiltonian cycle. 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 n-star, 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., the ring contains at least n! 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.