Edge-Recognizable Domination Numbers

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

Edge-recognizable domination numbers

For any undirected graph G, let zeta(G) be the collection of edge-deleted subgraphs. It is always possible to construct a graph H from zeta(G) so that zeta(H) = zeta(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. (C) 2003 Elsevier B.V. All rights reserved

Edge-Recognizable Domination Numbers

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