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Reconstructing a Graph from its Neighborhood Lists

Published online by Cambridge University Press:  12 September 2008

Martin Aigner  and
Eberhard Triesch
Martin Aigner
Affiliation:
Freie Universität Berlin, Fachbereich Mathematik, WE 2, Arnimallee 3, 1000 Berlin 33, Germany
Eberhard Triesch
Affiliation:
Forschungsinsitut für Diskrete Mathematik, Nassestraße 2, 5300 Bonn 1, Germany
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Abstract

Associate to a finite labeled graph G(V, E) its multiset of neighborhoods (G) = {N(υ): υ ∈ V}. We discuss the question of when a list is realizable by a graph, and to what extent G is determined by (G). The main results are: the decision problem is NP-complete; for bipartite graphs the decision problem is polynomially equivalent to Graph Isomorphism; forests G are determined up to isomorphism by (G); and if G is connected bipartite and (H) = (G), then H is completely described.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 2 , June 1993 , pp. 103 - 113
Copyright
Copyright © Cambridge University Press 1993

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References

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