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Longest Fault-Free Paths in Star Graphs with Edge Faults
September 2001 (vol. 50 no. 9)
pp. 960-971

Abstract—In this paper, we aim to embed longest fault-free paths in an n-dimensional star graph with edge faults. When $n\geq6$ and there are $n-3$ edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices, exclusive of two exceptions in which at most two vertices are excluded. Since the star graph is regular of degree $n-1$, $n-3$ (edge faults) is maximal in the worst case. When $n\geq6$ and there are $n-4$ edge faults, a longest fault-free path can be embedded between two arbitrary distinct vertices. The situation of $n<6$ is also discussed.

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Index Terms:
Bipartite graph, embedding, fault tolerance, Hamiltonicity, longest path, star graph.
Citation:
Sun-Yuan Hsieh, Gen-Huey Chen, Chin-Wen Ho, "Longest Fault-Free Paths in Star Graphs with Edge Faults," IEEE Transactions on Computers, vol. 50, no. 9, pp. 960-971, Sept. 2001, doi:10.1109/12.954510
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