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# Kocay's Lemma, Whitney's Theorem, and some Polynomial Invariant Reconstruction Problems

@article{Thatte2005KocaysLW, title={Kocay's Lemma, Whitney's Theorem, and some Polynomial Invariant Reconstruction Problems}, author={Bhalchandra D. Thatte}, journal={Electr. J. Comb.}, year={2005}, volume={12} }

- Published 2005 in Electr. J. Comb.

Given a graph G, an incidence matrix N (G) is defined on the set of distinct isomorphism types of induced subgraphs of G. It is proved that Ulam’s conjecture is true if and only if the N -matrix is a complete graph invariant. Several invariants of a graph are then shown to be reconstructible from its N -matrix. The invariants include the characteristic polynomial, the rank polynomial, the number of spanning trees and the number of hamiltonian cycles in a graph. These results are stronger than… CONTINUE READING