### 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-dimensional Möbius cube MQ_{n}, respectively, and let F = F_{v} ∪ F_{e}. In this paper, we show that MQ_{n} - F contains a fault-free Hamiltonian path when |F| ≤ n -1 and n ≥ 1. We also show that MQ_{n} -F is pancyclic when |F| ≤ n - 2 and n ≥ 2. Since MQ_{n} is regular of degree n, both results are optimal in the worst case.

Original language | English |
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Title of host publication | Proceedings - 11th International Conference on Parallel and Distributed Systems Workshops, ICPADS 2005 |

Editors | J. Ma, L.T. Yang |

Pages | 620-624 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2005 Sep 1 |

Event | 11th International Conference on Parallel and Distributed Systems Workshops, ICPADS 2005 - Fukuoka, Japan Duration: 2005 Jul 20 → 2005 Jul 22 |

### Publication series

Name | Proceedings of the International Conference on Parallel and Distributed Systems - ICPADS |
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Volume | 2 |

ISSN (Print) | 1521-9097 |

### Other

Other | 11th International Conference on Parallel and Distributed Systems Workshops, ICPADS 2005 |
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Country | Japan |

City | Fukuoka |

Period | 05-07-20 → 05-07-22 |

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture

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## Cite this

Hsieh, S. Y., & Chang, N. W. (2005). Cycle embedding on the Möbius cube with both faulty nodes and faulty edges. In J. Ma, & L. T. Yang (Eds.),

*Proceedings - 11th International Conference on Parallel and Distributed Systems Workshops, ICPADS 2005*(pp. 620-624). (Proceedings of the International Conference on Parallel and Distributed Systems - ICPADS; Vol. 2). https://doi.org/10.1109/ICPADS.2005.119