The edge reconstruction number of a disconnected graph

The edge reconstruction number of a graph G, RN(G), is the minimum number of edge deleted subgraphs required to determine G up to isomorphism. We prove the following results for a disconnected graph G with at least two nontrivial components. If G has a pair of nontrivial nonisomorphic components then RN (G) ≤ 3. If G has a pair of nontrivial nonisomorphic components, is not a forest, and contains a nontrivial component other than K3 or K1,3 then RN (G) ≤ 2. Finally, if all nontrivial components of G are isomorphic to a graph with k edges, then RN (G) ≤ k + 2. The edge reconstruction results in this paper are similar to the vertex reconstruction results stated by Myrvold (Ars Combinat. 28 (1989) 123-127), but a significant difference is that the edge reconstruction number of a disconnected graph is often two, while the vertex reconstruction number of a graph is always three or more. §