For any undirected graph G, let script l sign(G) be the collection of edge-deleted subgraphs. It is always possible to construct a graph H from script l sign(G) so that script l sign(H)=script l sign(G). The general edge-reconstruction conjecture states that G and H must be isomorphic if they have at least four edges. A graphical invariant that must be identical for all graphs that can be constructed from the given collection is said to be edge-recognizable. Here we show that the domination number and many of its common variations are edge-recognizable. © 2003 Elsevier B.V. All rights reserved.
Dutton, R. D., Brigham, R. C., & Gui, C. (2003). Edge-recognizable domination numbers. Discrete Mathematics, 272(1), 47–51. https://doi.org/10.1016/S0012-365X(03)00183-3