Vertex-switching reconstruction of subgraph numbers and triangle-free graphs (Q909676)

Let G be a graph with n vertices, and let S be a graph with k vertices, \(k<n/2\). Algebraic techniques are used to prove that the number of induced subgraphs (or just subgraphs) of G isomorphic to S is vertex- switching reconstructible. This vertex-switching version of Kelly's Lemma is used, along with structural arguments, to prove that triangle-free graphs are vertex-switching reconstructible.