Chordal 2-Connected Graphs and Spanning Trees

We present a transformation on a chordal 2-connected simple graph that decreases the number of spanning trees. Based on this transformation, we show that for positive integers n, m with n(n-1)/2 >= m >= 2n-3, the threshold graph Qn,m having n vertices and m edges that consists of an (n-k)-clique and k-1 vertices of degree 2 is the only graph with the fewest spanning trees among all 2-connected chordal graphs on n vertices and m edges.