Edge-recognizable domination numbers Original Research Article

For any undirected graph G, let C(G) be the collection of edge-deleted subgraphs. It is always possible to construct a graph H from C(G) so that C(H)=C(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.