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. [ABSTRACT FROM AUTHOR]