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Questions related to graph reconstruction, the problem of reconstructing a graph from a set or deck (multiset) of subgraphs.

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Reconstruction conjecture: Can other decks do the job?

I suspect that there are counterexamples to all three of your proposals. For example, you clarified that the distinguishing neighborhood of a vertex-transitive graph is just its 1-neighborhood. Then …
Timothy Chow's user avatar
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