Kelly's reconstruction conjecture for graphs

Let $G$ be a graph on $n$ vertices. For each vertex $v\in V(G)$, let $G_v$ be the subgraph obtained by deleting $v$ from $G$, and let

$$D(G)=\{G_v\mid v\in V(G)\}$$

be the multiset of all vertex-deleted subgraphs, called the deck. Kelly's reconstruction conjecture. Any two graphs $G$ and $H$ on $n>2$ vertices with equal multisets $D(G)$ and $D(H)$ are isomorphic. This is a classical open problem in graph theory: it asks whether a graph is determined up to isomorphism by its vertex-deleted subgraphs, although important special cases are known.