Proposed in 1942, the Graph Reconstruction Conjecture posits that every simple, finite, undirected graph with three or more vertices can be reconstructed up to isomorphism to the original graph, given the multiset of subgraphs produced by deleting each vertex along with its incident edges. Related to this Reconstruction Conjecture, existential reconstruction numbers,
We discuss the resulting data from calculating reconstruction numbers for all simple, undirected graphs with up to ten vertices. From this data, we establish the reasons behind all high existential reconstruction numbers (
We also consider 2-reconstructibility—the ability to reconstruct a graph
1970-2025 CP (Manitoba, Canada) unless otherwise stated.