On Family of Graphs with Minimum Number of Spanning Trees

We show that there is a well-defined family of connected simple graphs Λ(n, m) on n vertices and m edges such that all graphs in Λ(n, m) have the same number of spanning trees, and if ${G \in \Lambda(n, m)}$ then the number of spanning trees in G is strictly less than the number of spanning trees in any other connected simple graph ${H, H \notin \Lambda(n, m)}$ , on n vertices and m edges.