On the reconstraction of the matching polynomial and the reconstruction conjecture

[摘要] 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.

[关键词] matching;perfect matching;matching polynomial;matching matrix;reconstruction conjecture;edge reconstruction;node reconstruction.