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- Vladimir I. Levenshtein, Elena V. Konstantinova, Eugene Konstantinov, Sergey Molodtsov
- Discrete Applied Mathematics
- 2005

We prove that a connected graph of diameter at least 4 and of girth 7 or more (in particular, a tree) can be exactly reconstructed from metric balls of radius 2 of all its vertices. On the other hand, there exist graphs of diameter 3 and of girth 6 which are not reconstructible. This new graph theory problem is motivated by reconstruction of chemical… (More)

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