International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 155-162
On the reconstraction of the matching polynomial and the reconstruction conjecture
Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and Tobago
Received 30 May 1984; Revised 31 May 1985
Copyright © 1987 E. J. Farrell and S. A. Wahid. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.