Graphy Theory: Tesseract Representation

• To: mathgroup at smc.vnet.net
• Subject: [mg22842] Graphy Theory: Tesseract Representation
• From: "David Kazmer" <kazmer at ecs.umass.edu>
• Date: Sat, 1 Apr 2000 02:51:04 -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).

In the desired graph, the first column represents the
16 permutations corresponding to 4D coordinates.
The subsequent four columns represent each of the
four coordinates, with each of the two rows representing
the -1 and +1 levels of those states. Edges connect the
elements of the permutation to the four dimensions.

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

I believe that this graph could be constructed
very easily in Mathematica. Any ideas? Also, is
anyone aware of this type of graph being prevalent
in any domain? It has some interesting uses.

Best wishes, dave.

```

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