Reconstructing graphs

Abstract

Every graph G determines a collection M of maximal vertex proper subgraphs G i = G − v i {G_i} = G - {v_i} and a collection M’ of maximal edge proper subgraphs G i = G − e i {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.