### 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 |

### Fingerprint

### ASJC Scopus subject areas

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

### 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

**On some topological properties of hypercube, incomplete hypercube and supercube.** / Sen, Arunabha; Sengupta, A.; Bandyopadhyay, S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of 7th International Parallel Processing Symposium, IPPS 1993.*, 262806, Proceedings of 7th International Parallel Processing Symposium, IPPS 1993, Institute of Electrical and Electronics Engineers Inc., pp. 636-642, 7th International Parallel Processing Symposium, IPPS 1993, Newport, United States, 4/13/93. https://doi.org/10.1109/IPPS.1993.262806

}

TY - GEN

T1 - On some topological properties of hypercube, incomplete hypercube and supercube

AU - Sen, Arunabha

AU - Sengupta, A.

AU - Bandyopadhyay, S.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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)!.

AB - 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)!.

UR - http://www.scopus.com/inward/record.url?scp=85025287974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85025287974&partnerID=8YFLogxK

U2 - 10.1109/IPPS.1993.262806

DO - 10.1109/IPPS.1993.262806

M3 - Conference contribution

T3 - Proceedings of 7th International Parallel Processing Symposium, IPPS 1993

SP - 636

EP - 642

BT - Proceedings of 7th International Parallel Processing Symposium, IPPS 1993

PB - Institute of Electrical and Electronics Engineers Inc.

ER -