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    STUDIA MATHEMATICA - Issue no. 4 / 2014  
         
  Article:   RECONSTRUCTING GRAPHS FROM A DECK OF ALL DISTINCT CARDS.

Authors:  . 		 
       
         
  Abstract:   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 of its induced subgraphs is formulated. Finally, it is shown that graphs having a deck free from duplicate cards are reconstructible.

Mathematics Subject Classification (2010): 05C60, 18D10.
Keywords: Graph reconstruction, card equivalence, automorphism equivalence, relative degree sequences, traced monoidal categories.
  
         
     
         
         
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