10176

# Kneser Graphs

Imagine a set of dominos with strings connecting the dominoes that share a number. Could this mess of strings be laid out nicely? More formally, is there a nice embedding for a graph based on connecting unordered tuples from {1, ..., n}? Graphs of this type are known as Kneser graphs.
Compose the cyclic permutations (12345678) and (13527486) repeatedly: (12345678), (13527486), (15738264), (17856342), (18674523), (16482735), and (14263857). When these are partitioned into unordered tuples, (e.g., (12345678) becomes (12), (34), (56), (78)), each tuple appears exactly once. The permutation (13527486) is thus special. This Demonstration uses preselected permutations to provide nice pictures of these graphs.
Miraculously, these same permutations are used by the Central Council of Church Bell Ringers. For graph order 12 ("Maximus", for a bell ringer) the selected permutations are a partial set.

### 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.