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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 G = (V,E), a vertex-deleted subgraph of G is a subgraph formed by deleting exactly one vertex from G. Clearly, it is an induced subgraph of G. For a graph G, the deck of G, denoted D(G), is the multiset of all vertex-deleted subgraphs of G. Each graph in D(G) is called a card. Two graphs that have the same deck are said to be hypomorphic.