Reconstructing graphs from a deck of all distinct cards

  title={Reconstructing graphs from a deck of all distinct cards},
  author={Mikl{\'o}s Bartha and Amitesh S. Shuva},
The graph reconstruction conjecture is looked at from a new perspective. Given a graph G, three equivalence relations are considered on V (G): card equivalence, automorphism equivalence, and the equivalence of having the same behavior. A structural characterization of card equivalence in terms of automorphism equivalence is worked out. Relative degree-sequences of subgraphs of G are introduced, and a new conjecture aiming at the reconstruction of G from the multiset of relative degree-sequences… CONTINUE READING

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