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Hypomorphisms, orbits, and reconstruction. (English)
J. Comb. Theory, Ser. B 44, No.2, 187-200 (1988).
Graphs G and H are hypomorphic if there is a bijection $ϕ$ : V(G)$\to V(H)$ such that G-u$\cong H-ϕ(u)$, for all $u\in V(G)$. The reconstruction conjecture states that hypomorphic graphs are isomorphic, if G has at least three vertices. We investigate properties of the isomorphisms G-u$\cong H-ϕ(u)$, and their relation to the reconstructibility of G.