On the reconstraction of the matching polynomial and the reconstruction conjecture - E. J. Farrell; S. A. Wahid (International Journal of Mathematics and Mathematical Sciences)
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.