We consider two seemingly related problems. The first concerns pairs of graphs \(G\) and \(H\) containing endvertices (vertices of degree \(1\)) and having the property that, although they are not isomorphic, they have the same collection of endvertex-deleted subgraphs.
The second question concerns graphs \(G\) containing endvertices and having the property that, although no two endvertices are similar, any two endvertex-deleted subgraphs of \(G\) are isomorphic.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.