Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults

Authors:
Sun-Yuan Hsieh;Chang-De Wu
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 70101;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 70101
Venue:
The Journal of Supercomputing
Year:
2009

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Abstract

The star graph is viewed as an attractive alternative to the hypercube. In this paper, we investigate the Hamiltonicity of an n-dimensional star graph. We show that for any n-dimensional star graph (n驴4) with at most 3n驴10 faulty edges in which each node is incident with at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves on the previously best known result for the case where the number of tolerable faulty edges is bounded by 2n驴7. We also demonstrate that our result is optimal with respect to the worst case scenario, where every other node of a cycle of length 6 is incident with exactly n驴3 faulty noncycle edges.