Reconstruction of a graph from 2-vicinities of its vertices

Authors:
Vladimir Levenshtein;Elena Konstantinova;Eugene Konstantinov;Sergey Molodtsov
Affiliations:
Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Miusskaya sq. 4, 125047 Moscow, Russia;Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Pr. Koptuyga 4, 630090 Novosibirsk,Russia;Budker Institute of Nuclear Physics, Siberian Branch of Russian Academy of Sciences, Pr. Lavrent'eva 11, 630090 Novosibirsk, Russia;Vorozhtsov Institute of Organic Chemistry, Siberian Branch of Russian Academy of Sciences, Pr. Lavrent'eva 9, 630090 Novosibirsk, Russia
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 3
Cited 1

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Abstract

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 compounds.