A sufficient condition for Set Reconstruction

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 all graphs are set reconstructible if all \(2\)-connected graphs \(G\) with \(diam(G) = 2\) and all \(2\)-connected graphs \(G\) with \(diam(G) = diam(\overline{G}) = 3\) are set reconstructible.