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Reductions of the graph reconstruction conjecture

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
36
Issue
1
Identifiers
DOI: 10.1016/0012-365x(81)90177-1
Disciplines
  • Mathematics

Abstract

Abstract In this note we shall show that the Graph Reconstruction Conjecture (also called the Kelly-Ulam conjecture [1, p. 11]) is equivalent to a conjecture about the algebraic properties of certain directed trees and their homomorphic images. We shall show the the Greph Reconstruction Conjecture is equivalent to recognizing the (abstract) group of a graph from the tree (generalized “deck”) of the graph.

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