### Abstract

Hamiltonian properties of hypercube, incomplete hypercube and supercube are examined. It is known that in a nonfaulty hypercube there are at least n! Hamiltonian cycles. The authors extend this result showing that the lower bound is at least 2/sup n-3/n! They show that with at most n-2 faulty links a faulty hypercube has at least 2(n-2)! Hamiltonian cycles. They establish that an incomplete hypercube with odd (even) number of nodes has (n-2)! Hamiltonian paths (cycles). They show that a supercube has at least (n-1)! Hamiltonian cycles and when the number of nodes is 2/sup n-1/+2/sup n-2/, then the number of Hamiltonian cycles is at least as high as 2(n-1)!.

Original language | English (US) |
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Title of host publication | Proceedings of 7th International Parallel Processing Symposium, IPPS 1993 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 636-642 |

Number of pages | 7 |

ISBN (Electronic) | 0818634421, 9780818634420 |

DOIs | |

State | Published - Jan 1 1993 |

Event | 7th International Parallel Processing Symposium, IPPS 1993 - Newport, United States Duration: Apr 13 1993 → Apr 16 1993 |

### Publication series

Name | Proceedings of 7th International Parallel Processing Symposium, IPPS 1993 |
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### Conference

Conference | 7th International Parallel Processing Symposium, IPPS 1993 |
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Country | United States |

City | Newport |

Period | 4/13/93 → 4/16/93 |

### ASJC Scopus subject areas

- Computer Science Applications
- Hardware and Architecture
- Software
- Computational Theory and Mathematics
- Computer Networks and Communications

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## Cite this

*Proceedings of 7th International Parallel Processing Symposium, IPPS 1993*(pp. 636-642). [262806] (Proceedings of 7th International Parallel Processing Symposium, IPPS 1993). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IPPS.1993.262806