AbstractFor every positive integerc, we construct a pairGc,Hcof infinite, nonisomorphic graphs both having exactlyccomponents such thatGcandHcare hypomorphic, i.e.,GcandHchave the same families of vertex‐deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pairG1,H1is 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 g