### Abstract

The k-ary n-cube has been used as the underlying topology for most practical multicomputers, and has been extensively studied in the past. In this paper, we investigate some properties of this network. In particular, we study the problem of finding the number of nodes located i hops away from a given node (surface area) and the number of nodes located within i hops away from a given node (volume) in both the unidirectional and bidirectional k-ary n-cube, and have derived exact expressions calculating these numbers. These results are very useful when studying, for example, the spanning tree structure of the k-ary n-cube and the problem of resource placement in this network.

Original language | English |
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Title of host publication | Proceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS |

Pages | 517-524 |

Number of pages | 8 |

Publication status | Published - 2001 |

Event | 8th International Conference on Parallel and Distributed Systems - Kyongju, Korea, Republic of Duration: Jun 26 2001 → Jun 29 2001 |

### Other

Other | 8th International Conference on Parallel and Distributed Systems |
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Country | Korea, Republic of |

City | Kyongju |

Period | 6/26/01 → 6/29/01 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS*(pp. 517-524)

**On some properties of k-ary n-cubes.** / Sarbazi-Azad, H.; Ould-Khaoua, M.; Mackenzie, L. M.; Akl, S. G.

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

*Proceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS.*pp. 517-524, 8th International Conference on Parallel and Distributed Systems, Kyongju, Korea, Republic of, 6/26/01.

}

TY - GEN

T1 - On some properties of k-ary n-cubes

AU - Sarbazi-Azad, H.

AU - Ould-Khaoua, M.

AU - Mackenzie, L. M.

AU - Akl, S. G.

PY - 2001

Y1 - 2001

N2 - The k-ary n-cube has been used as the underlying topology for most practical multicomputers, and has been extensively studied in the past. In this paper, we investigate some properties of this network. In particular, we study the problem of finding the number of nodes located i hops away from a given node (surface area) and the number of nodes located within i hops away from a given node (volume) in both the unidirectional and bidirectional k-ary n-cube, and have derived exact expressions calculating these numbers. These results are very useful when studying, for example, the spanning tree structure of the k-ary n-cube and the problem of resource placement in this network.

AB - The k-ary n-cube has been used as the underlying topology for most practical multicomputers, and has been extensively studied in the past. In this paper, we investigate some properties of this network. In particular, we study the problem of finding the number of nodes located i hops away from a given node (surface area) and the number of nodes located within i hops away from a given node (volume) in both the unidirectional and bidirectional k-ary n-cube, and have derived exact expressions calculating these numbers. These results are very useful when studying, for example, the spanning tree structure of the k-ary n-cube and the problem of resource placement in this network.

UR - http://www.scopus.com/inward/record.url?scp=0034851199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034851199&partnerID=8YFLogxK

M3 - Conference contribution

SP - 517

EP - 524

BT - Proceedings of the Internatoinal Conference on Parallel and Distributed Systems - ICPADS

ER -