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Graph Theory: 2D Tesseract Representation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22824] Graph Theory: 2D Tesseract Representation
  • From: "David Kazmer" <kazmer at ecs.umass.edu>
  • Date: Fri, 31 Mar 2000 01:01:26 -0500 (EST)
  • Organization: College of Engineering, University of Massachusetts
  • Sender: owner-wri-mathgroup at wolfram.com

Here's a potentially interesting problem. I wish
to represent a Tesseract, a 4D cube with +/-1
vertices, as a 2D graph. This graph also represents
a full factorial design of experiments (my
interest).

I know how to do it, but there is a quesiton of
efficiency. You could:
1. Construct CompleteGraph[16, 2, 2, 2, 2], then
2. Remove edges using exhaustive edge checks.

In this graph, the first column represents the
permutation corresponding to 4D coordinates.
Edges connect the elements of the permutation
to the -1 and +1 levels of the four subsequent
dimensions.

I believe that this graph could be constructed
very easily. Any ideas?

Best wishes, dave.




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