Embed a Longest Path between Arbitrary Two Vertices of a Faulty Star Graph

@inproceedings{Hsieh2000EmbedAL,
  title={Embed a Longest Path between Arbitrary Two Vertices of a Faulty Star Graph},
  author={Sun-Yuan Hsieh and Gen-Huey Chen},
  year={2000}
}
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 can embed a fault−free path of length n!-2|Fv|−2 (n!-2|Fv|−1, respectively) between arbitrary two vertices of even (odd, respectively) distance. Since Sn is bipartite with two partite sets of equal size, the embedded path is… CONTINUE READING

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