File:3-bit Walsh permutations; Cayley 136 421.svg

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Summary

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Description
Abstraction of the Cayley graph: The 28 vertices are labelled with sets (rather than tuples), and each one corresponds to 6 Cayley graph vertices.

Cayley graph of the general linear group GL(3,2)

136 is the Gray code and 421 is the bit-reversal permutation.
The 168 directed edges correspond to the former, the 84 undirected edges to the latter.

The node colors represent the six conjugacy classes.

The graph is embedded on a torus. Parallel dashed borders are identical ("glued together").

The graph is drawn in 6 repeating units, each corresponding to the smaller graph shown on the right.
The red/green edges in the abstraction correspond to directed/undirected edges in the Cayley graph.
The normal green edges correspond to thin dark gray edges, and the green loops to thick light gray between units.

Mirrored triples are centrally symmetric to each other.

The older version contains searchable text.
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
Other versions
determinant and cluster colors
different representation with redundant squares

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Date/TimeThumbnailDimensionsUserComment
current12:18, 22 August 2022Thumbnail for version as of 12:18, 22 August 20222,402 × 2,097 (677 KB)Watchduck (talk | contribs)text to path (Ubuntu Condensed)
11:15, 22 August 2022Thumbnail for version as of 11:15, 22 August 20222,402 × 2,097 (455 KB)Watchduck (talk | contribs)Uploaded own work with UploadWizard

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