Spanning trees of generalized cones and bipartite graphs

We compute the number of spanning trees for the generalized cone of the complete graph Kn and a number of families of some modified bipartite graphs K{m,n}. Our method provides alternate ways of obtaining the classical formulas for finding the number of spanning trees of Kn and K{m,n}. The method relies on the vertex deletion formula for the number of spanning trees, which is a recently developed technique to compute the number of spanning trees.