A reconstructible graph is a graph for which 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 4 to 13 vertices.
