Reconstruction conjecture

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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 , a vertex-deleted subgraph of is a subgraph formed by deleting exactly one vertex from . Clearly, it is an induced subgraph of .

For a graph , the deck of G, denoted , is the multiset of all vertex-deleted subgraphs of . Each graph in is called a card. Two graphs that have the same deck are said to be hypomorphic.

With these definitions, the conjecture can be stated as:

Harary suggested a stronger version of the conjecture:

Given a graph , an edge-deleted subgraph of is a subgraph formed by deleting exactly one edge from .

This page was last edited on 11 November 2017, at 10:54.
Reference: https://en.wikipedia.org/wiki/Reconstruction_conjecture under CC BY-SA license.

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