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Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes. (English) Zbl 1132.68019
Summary: The hypercube has been one of the most popular interconnection networks for parallel computer/communication systems. In this paper, we assume that each node is incident with at least two fault-free links. Under this assumption, we show that every fault-free edge lies on a fault-free cycle of every even length from 6 to 2 n inclusive, even if it has up to 2n-5 link faults. The result is optimal with respect to the number of link faults tolerated.
MSC:
68M15Reliability, testing and fault tolerance computer systems
68M10Network design and communication of computer systems
68R10Graph theory in connection with computer science (including graph drawing)