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Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures
December 1997 (vol. 8 no. 12)
pp. 1185-1195

Abstract—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 fen− 3 faulty links, a Hamiltonian cycle still can be found in an n-star, and that with fvn− 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 + fvn− 3, our embedding is able to establish a ring containing at least n! − 4fv nodes.

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Index Terms:
Fault tolerance, graph embedding, Hamiltonian cycle, interconnection network, processor allocation, ring, star graph.
Citation:
Yu-Chee Tseng, Shu-Hui Chang, Jang-Ping Sheu, "Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 12, pp. 1185-1195, Dec. 1997, doi:10.1109/71.640010
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