Fault diameter of k-ary n-cube networks

Khaled Day*, Abdel Elah Al-Ayyoub

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

131 Citations (Scopus)


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 languageEnglish
Pages (from-to)903-907
Number of pages5
JournalIEEE Transactions on Parallel and Distributed Systems
Issue number9
Publication statusPublished - 1997


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

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Computational Theory and Mathematics


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