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Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges
July 2006 (vol. 55 no. 7)
pp. 854-863
A graph G=(V,E) is said to be pancyclic if it contains fault-free cycles of all lengths from 4 to |V| in G. Let F_{v} and F_{e} be the sets of faulty nodes and faulty edges of an n{\hbox{-}}{\rm dimensional} Möbius cube MQ_{n}, respectively, and let F=F_{v}\cup F_{e}. A faulty graph is pancyclic if it contains fault-free cycles of all lengths from 4 to |V-F_{v}|. In this paper, we show that MQ_{n}-F contains a fault-free Hamiltonian path when |F|\leq n-1 and n\geq 1. We also show that MQ_{n}-F is pancyclic when |F|\leq n-2 and n\geq 2. Since MQ_{n} is regular of degree n, both results are optimal in the worst case.

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Index Terms:
Graph-theoretic interconnection networks, Möbius cubes, fault-tolerant embedding, pancyclicity, Hamiltonian.
Sun-Yuan Hsieh, Nai-Wen Chang, "Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges," IEEE Transactions on Computers, vol. 55, no. 7, pp. 854-863, July 2006, doi:10.1109/TC.2006.104
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