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.