Reconstruction conjecture

Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam.

Given a graph ${\displaystyle G=(V,E)}$, a vertex-deleted subgraph of ${\displaystyle G}$ is a subgraph formed by deleting exactly one vertex from ${\displaystyle G}$. Clearly, it is an induced subgraph of ${\displaystyle G}$.

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