### Abstract

We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained in [8] where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.

Original language | English |
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Pages (from-to) | 903-907 |

Number of pages | 5 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 8 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1997 |

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### Keywords

- Fault diameter
- Interconnection networks
- K-ary n-cube
- Node-disjoint paths
- Torus

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*8*(9), 903-907. https://doi.org/10.1109/71.615436