Graphs with all spanning trees nonisomorphic Original Research Article

The paper presents some results on graphs that do not have two distinct isomorphic spanning trees. It is proved that any such connected graph with at least two vertices must have the property that each end-block has just one edge. On the other hand, the class of such graphs is quite large; it is shown that any graph is an induced subgraph of a connected graph without two distinct, isomorphic spanning trees.