Embedding longest fault-free paths onto star graphs with more vertex faults

  • Authors:

  • Sun-Yuan Hsieh

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Cheng Kung University, No.1, Ta-Hsueh Road, Tainan 701, Taiwan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2005

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Abstract

The n-dimensional star graph Sn belongs to a class of bipartite graphs, and it is 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 F(Sn) be the set of vertex faults. Previously, it was shown that when |F(Sn)| ≤ n -5, Sn with n ≥ 6 can embed a longest fault-free path of length at least n! -2|F(Sn)| -1 (respectively, n! -2|F(Sn)| -2) between two arbitrary vertices in different partite sets (respectively, the same partite set) [Longest fault-free paths in star graphs with vertex faults, Theoretical Computer Science 262 (2001) 215-227]. In this paper, we improve the above result by tolerating more faults (|F(Sn)|≤ n -3) to embed a longest fault-free path between two arbitrary vertices in Sn, n ≥ 4.