AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.4 din 2014 | |||||||
Articol: |
RECONSTRUCTING GRAPHS FROM A DECK OF ALL DISTINCT CARDS. Autori: . |
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Rezumat:
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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