Rock-Paper-Scissors Meets Borromean Rings

  title={Rock-Paper-Scissors Meets Borromean Rings},
  author={Marc Chamberland and Eugene A. Herman},
  journal={The Mathematical Intelligencer},
Directed graphs with an odd number of vertices n, where each vertex has both (n − 1)/2 incoming and outgoing edges, have a rich structure. We were lead to their study by both the Borromean rings and the game rockpaper-scissors. An interesting interplay between groups, graphs, topological links, and matrices reveals the structure of these objects, and for larger values of n, extensive computation produces some surprises. Perhaps most surprising is how few of the larger graphs have any symmetry… 
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Generating regular directed graphs
  • G. Brinkmann
  • Computer Science, Mathematics
    Discret. Math.
  • 2013
An algorithm to efficiently generate all regular directed graphs for a given number of vertices and given degree is described. Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112, E-mail address: chamberl@math.grinnell
  • edu Department of Mathematics and Statistics