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}
}
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