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ABSTRACT
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.
INDEX TERMS
Graph-theoretic interconnection networks, Möbius cubes, fault-tolerant embedding, pancyclicity, Hamiltonian.
CITATION

N. Chang and S. Hsieh, "Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges," in IEEE Transactions on Computers, vol. 55, no. , pp. 854-863, 2006.
doi:10.1109/TC.2006.104
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