Longest fault-free paths in star graphs with vertex faults.
Journal
Theor. Comput. Sci.
Journal Volume
262
Journal Issue
1
Pages
215-227
Date Issued
2001
Author(s)
Abstract
The star graph Sn has been recognized as an attractive alternative to the hypercube. Since S1, S2, and S3 have trivial structures, we focus our attention on Sn with n ≥ 4 in this paper. Let Fv denote the set of faulty vertices in Sn. We show that when |Fv| ≤ n - 5 ,Sn with n ≥ 6 contains a fault-free path of length n! - 2|Fv| - 2 (n! - 2 |Fv| - 1) between arbitrary two vertices of even (odd) distance. Since Sn is bipartite with two partite sets of equal size, the path is longest for the worst-case scenario. The situation of n ≥ 4 and |Fv| ≥ n - 5 is also discussed. © 2001 Elsevier Science B.V. All rights reserved.
Type
journal article