Embeddings of cycles, meshes and tori in faulty k-ary n-cubes

  • Authors:

  • Yaagoub Ashir;Iain A. Stewart

  • Affiliations:

  • -;-

  • Venue:
  • ICPADS '97 Proceedings of the 1997 International Conference on Parallel and Distributed Systems
  • Year:
  • 1997

Quantified Score

Hi-index 0.00

Visualization

Abstract

We investigate the existence of cycles, meshes and tori in a k-ary n-cube Q/sub n//sup k/ in which a limited number of nodes and links are faulty. Our main result is that in a k-ary n-cube Q/sub n//sup k/ in which there are v faulty nodes /spl lambda/faulty links where v+/spl lambda//spl les/n, there is a cycle of length at least k/sup n/-vw, where w=1 if k is odd and w=2 if k is even (throughout k/spl ges/3 and n/spl ges/2). We extend this result so as to prove the existence of large meshes and tori in such a faulty k-ary n-cube.