A graph is reconstructible if every graph with the same graph deck is isomorphic to it. Equivalently, a graph is reconstructible if it has no nonisomorphic hypomorphic mate.
This is different from full reconstructibility, where the graph is determined instead by squared edge-length data from placements in a specified dimension.
The graph reconstruction conjecture asserts that every simple finite graph on at least three vertices is reconstructible.
McKay (2022) computationally verified reconstructibility for all graphs with at most 13 vertices.
