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.
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