10178

Prüfer Encoding of Labeled Trees

A Prüfer sequence of length , for , is any sequence of integers between 1 and with repetitions allowed. There is a one-to-one correspondence between the set of labeled trees with vertices and the Prüfer sequences of length , from which is derived Cayley's formula that counts the number of labeled trees of vertices, namely . This Demonstration shows the Prüfer sequence of random labeled trees of a chosen number of vertices. The procedure is as follows. Choose a leaf (a vertex of degree 1) with the smallest label and write down the label of its only neighbor. Then eliminate the leaf from the tree and repeat the process. This sequence of labels forms the Prüfer coding of the tree. If we count the number of occurrences of a number in this sequence, it equals the degree of its vertex minus 1.

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.