Counting labeled trees

This lecture covers the counting of labeled trees using Prüfer codes, providing an easy formula and proof. It explains an algorithm to convert trees to sequences and vice versa, known as Algorithm 2. The lecture demonstrates the application of Algorithm 1 and Algorithm 2, showing how they provide maps between trees and sequences. The proof of the theorems is done by induction, starting with the base case of n=2. The lecture concludes with exercises on determining the Prüfer code of a tree and the appearance of vertices in the code.