All Graphs are Set Reconstructible if all \(2\)-Connected Graphs are Set Reconstructible

Abstract

A graph is called set reconstructible if it is determined uniquely (up to isomorphism) by the set of its vertex-deleted subgraphs. We prove that some classes of separable graphs with a unique endvertex are set reconstructible and show that all graphs are set reconstructible if all \(2\)-connected graphs are set reconstructible.