Note on the reconstruction of infinite graphs with a fixed finite number of components

For every positive integer c, we construct a pair G_c, H_c of infinite, nonisomorphic graphs both having exactly c components such that G_c and H_c are hypomorphic, i.e., G_c and H_c have the same families of vertex-deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pair G₁, H₁ is an example for a pair of non-isomorphic, hypomorphic, connected graphs also having connected complements—a property not shared by any of the previously known counterexamples to the reconstruction conjecture for infinite graphs.