Counting Spanning Trees

For a connected graph g, let τ(g) be the number of spanning trees in g. cayley’s formula gives asimple expression for τ(kn), where kn is the complete graph of order n. in this talk, i will introducesome extensions of cayley’s formula, which include formulas for τ(l(g)) and τ(m(g)) for an arbitrarygraph g, where l(g) and m(g) are the line graph and the middle graph of g respectively. i will alsopresent some known results and unsolved problems related to τ(g).