Prüfer-Like Codes for Labeled Trees

In 1918 Prüfer showed a one-to-one correspondence between n-node labeled trees and (n – 2)-tuples of node labels. The proof employed a tree code, computed by iteratively deleting the leaf with the smallest label and recording its neighbor. Since then other tree codes have been proposed, based on different node deletion sequences. These codes have different properties, interesting and useful in graph theory and computer science. In this paper we survey and classify these Prüfer-like codes as well as new codes based on the parameter values of the proposed generic tree-encoding algorithm and study their properties.