# reconstruction

## Switching reconstruction conjecture ★★

Author(s): Stanley

**Conjecture**Every simple graph on five or more vertices is switching-reconstructible.

Keywords: reconstruction

## Edge Reconstruction Conjecture ★★★

Author(s): Harary

**Conjecture**

Every simple graph with at least 4 edges is reconstructible from it's edge deleted subgraphs

Keywords: reconstruction

## Reconstruction conjecture ★★★★

The *deck* of a graph is the multiset consisting of all unlabelled subgraphs obtained from by deleting a vertex in all possible ways (counted according to multiplicity).

**Conjecture**If two graphs on vertices have the same deck, then they are isomorphic.

Keywords: reconstruction

## Graham's conjecture on tree reconstruction ★★

Author(s): Graham

**Problem**for every graph , we let denote the line graph of . Given that is a tree, can we determine it from the integer sequence ?

Keywords: reconstruction; tree