Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631367 | Applied Mathematics and Computation | 2012 | 5 Pages |
Abstract
The class of k-ary n-cubes represents the most commonly used interconnection topology for distributed-memory parallel systems. Given an even k ⩾ 4, let (V1, V2) be the bipartition of the k-ary 2-cube, fv1, fv2 be the numbers of faulty vertices in V1 and V2, respectively, and fe be the number of faulty edges. In this paper, we prove that there exists a cycle of length k2 â 2max{fv1, fv2} in the k-ary 2-cube with 0 ⩽ fv1 + fv2 + fe ⩽ 2. This result is optimal with respect to the number of faults tolerated.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Shiying Wang, Kai Feng, Shurong Zhang, Jing Li,