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

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2 Author(s)
Ashir, Y.A. ; Dept. of Math. & Comput. Sci., Leicester Univ., UK ; Stewart, I.A.

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

Published in:

Parallel and Distributed Systems, 1997. Proceedings., 1997 International Conference on

Date of Conference:

10-13 Dec 1997