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<p><b>Abstract</b>—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 <it>f</it><sub><it>e</it></sub>≤<it>n</it>− 3 faulty links, a Hamiltonian cycle still can be found in an <it>n</it>-star, and that with <it>f</it><sub><it>v</it></sub>≤<it>n</it>− 3 faulty nodes, a ring containing at most 4<it>f</it><sub><it>v</it></sub> nodes less than that in a Hamiltonian cycle can be found (i.e., the ring contains at least <it>n</it>! − 4<it>f</it><sub><it>v</it></sub> nodes). In general, in an <it>n</it>-star with <it>f</it><sub><it>e</it></sub> faulty links and <it>f</it><sub><it>v</it></sub> faulty nodes, where <it>f</it><sub><it>e</it></sub> + <it>f</it><sub><it>v</it></sub>≤<it>n</it>− 3, our embedding is able to establish a ring containing at least <it>n</it>! − 4<it>f</it><sub><it>v</it></sub> nodes.</p>
Fault tolerance, graph embedding, Hamiltonian cycle, interconnection network, processor allocation, ring, star graph.
Jang-Ping Sheu, Shu-Hui Chang, Yu-Chee Tseng, "Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures", IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 1185-1195, December 1997, doi:10.1109/71.640010
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