10176

# Prüfer Codes of Labeled Trees

In 1889, Cayley proved that there are labeled trees on nodes. In 1918, Prüfer found a method for constructing each tree.
Consider the tree with code {2, 8, 9, 4, 7, 7, 2} that is given as the default tree in this Demonstration. The first digit of the Prüfer code is the branch that has the smallest isolated number. Pruning that branch gives a new tree, and the process repeats, as shown in the Details.

### DETAILS

The smallest non-branch number is 1. Cut it from 2.
The smallest non-branch number is 3. Cut it from 8.
The smallest non-branch number is 5. Cut it from 9.
The smallest non-branch number is 6. Cut it from 4.
The smallest non-branch number is 4. Cut it from 7.
The smallest non-branch number is 8. Cut it from 7.
The smallest non-branch number is 7. Cut it from 2.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.