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On the reconstraction of the matching polynomial and the reconstruction conjecture

DOI: 10.1155/s016117128700019x

Keywords: matching , perfect matching , matching polynomial , matching matrix , reconstruction conjecture , edge reconstruction , node reconstruction.

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Two results are proved. (i) It is shown that the matching polynomial is both node and edge reconstructable. Moreover a practical method of reconstruction is given. (ii) A technique is given for reconstructing a graph from its node-deleted and edge-deleted subgraphs. This settles one part of the Reconstruction Conjecture.


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