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Published online by Cambridge University Press: 09 April 2009
Let Γ be a graph with isomorphic subgraphs G and H, and let θ: G → H be an isomorphism. If θ can be extended to an automorphism of Γ, we call θ a partial automorphism of Γ.
We consider the application of partial automorphisms to the graph reconstruction conjecture, in particular, to the problem of reconstructing graphs with two vertices of degree k – 1 and the remaining vertices of degree k.