Graphs with all spanning trees nonisomorphic
If a connected graph \(G\) with at least two vertices has the property that all its spanning trees are pairwise nonisomorphic, then every end-block of \(G\) has just one edge. This is one of the main results of this paper. By an easy construction it is shown that any graph is an induced subgraph of a connected graph without two distinct isomorphic spanning trees. Generalizations of this construction lead to some related results.
scientific article; zbMATH DE number 932519