Verification
Both the reconstruction and set reconstruction conjectures have been verified for all graphs with at most 11 vertices (McKay).
In a probabilistic sense, it has been shown (Bollobás) that almost all graphs are reconstructible. This means that the probability that a randomly chosen graph on vertices is not reconstructible goes to 0 as goes to infinity. In fact, it was shown that not only are almost all graphs reconstructible, but in fact that the entire deck is not necessary to reconstruct them — almost all graphs have the property that there exist three cards in their deck that uniquely determine the graph.
Read more about this topic: Reconstruction Conjecture
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