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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Reconstructing graphs


Author: D. L. Greenwell
Journal: Proc. Amer. Math. Soc. 30 (1971), 431-433
MSC: Primary 05.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0286699-3
MathSciNet review: 0286699
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Abstract: Every graph G determines a collection M of maximal vertex proper subgraphs $ {G_i} = G - {v_i}$ and a collection M' of maximal edge proper subgraphs $ {G^i} = G - {e_i}$. In this paper we prove that a graph G, on at least three edges and without isolated vertices, can be reconstructed, up to isomorphism, from the collection M' if it can be reconstructed, up to isomorphism, from the collection M.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0286699-3
Keywords: Vertex problem, edge problem, line graph, iterated line graph
Article copyright: © Copyright 1971 American Mathematical Society