Abstract.
An edge e of a graph G is said to be a fixed edge if G−e+e ′≅G implies that e ′=e, and a forced edge if G−e+e ′ is an edge-reconstruction of G implies that e ′=e. In this paper, we use the method of excludable configurations to investigate the fixed edges and the forced edges of series-parallel networks. It is proved that all series-parallel networks contain fixed edges except P 3∨K 1 and P 4∨K 1, and that all series-parallel networks are edge-reconstructible.
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Received: December 22, 1997 Final version received: July 21, 1999
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Fan, H., Wu, YL. & Wong, C. On Fixed Edges and Edge-Reconstruction of Series-Parallel Networks. Graphs Comb 17, 213–225 (2001). https://doi.org/10.1007/PL00007242
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DOI: https://doi.org/10.1007/PL00007242