Combinatorial Analysis of the Fault-Diameter of the N-Cube

  • Authors:
  • S. Latifi

  • Affiliations:
  • -

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1993

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Abstract

It is shown that the diameter of an n-dimensional hypercube can only increase by an additive constant of 1 when (n-1) faulty processors are present. Based on the concept of forbidden faulty sets, which guarantees the connectivity of the cube in the presence of up to (2n-3) faulty processors. It is shown that the diameter of the n-cube increases to (n-2) as a result of (2n-3) processor failures. It is also shown that only those nodes whose Hamming distance is (n-2) have the potential to be located at two ends of the diameter of the damaged cube. It is proven that all the n-cubes with (2n-3) faulty processors and a fault-diameter of (n+2) are isomorphic. A generalization to the subject study is presented.