A New Proof of Cayleyʼs Formula for Labeled Spanning Trees

Cayleysʼs formula for enumerating spanning trees in complete graphs is one of the main theorems in this topic. In this note based on a new recursive method for the enumeration of spanning trees and meanwhile enumerating spanning trees in a kind of complete multigraph, a new proof for the Cayleyʼs formula is given. A generalization of this formula is also presented.