Conditional edge-fault-tolerant Hamiltonian cycle embedding of star graphs

Abstract

The star graph has been recognized as an attractive alternative to the hypercube. In this paper, we investigate the hamiltoncity of a n-dimensional star graph. We show that for any n-dimensional star graph (n ≥ 4) with at most 3n − 10 faulty edges in which each node is incident to at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves the previously best known result where the number of tolerable faulty edges is bounded by 2n − 7. We also demonstrate that our result is optimal with respect to the worst case scenario where every other node of a six-length cycle is incident to exactly n − 3 faulty non-cycle edges.