Talk:Clebsch graph

"In an n-dimensional hypercube, a pair of vertices are opposite if the shortest path between them has length n."

Shouldn't that be "the square root of n" (assuming unit-length edges)? AnonMoos (talk) 17:05, 28 January 2011 (UTC)

I reworded it to make it more obvious that graph length (number of edges) rather than any kind of Euclidean distance was intended here. —David Eppstein (talk) 17:54, 28 January 2011 (UTC)

Two Clebsch graphs or one?

I disagree that the 10-regular graph described here should be described as "Clebsch graph":

• Clebsch, in his original paper http://eudml.org/doc/148055 , explicitly gives the edges of the 5-regular one on page 144;
• Wolfram describes using "Clebsch graph" for the 10-regular one as "confusing";
• most of the English article (including the infobox and the illustrations) is indeed about the 5-regular one;
• all other wikipedias consider only the 5-regular graph.

The 10-regular graph can be described as "named Clebsch graph by some authors", so we don't completly ignore Seidel and Brouwer. That's what I did on the French Wikipedia, in a paragraph named "Complementary of the Clebsch graph".

If you stick to the "two graphs" approach, which I do not advice, then this article should be renamed "Clebsch graphs", since there would be two of them, and by analogy with the other articles that describe two or more graphs.

Best, --MathsPoetry (talk) 08:17, 27 April 2013 (UTC)

Seidel gave the original definition, following Coxeter. His definition was used by all authors (e.g. Goethals, Neumaier, Mulder) until halfway the '80s. Maybe the confusion was started by Cameron & van Lint, Designs, graphs, codes and their links, who write explicitly that their definition of the Clebsch and Schlaefli graphs is the complement of Seidel's. In Goldbach & Claasen, On splitting the Clebsch graph (1994), Seidel's original definition is used, but the MR review (incorrectly) uses the complementary one.

2001:980:3FF4:1:7A24:AFFF:FE88:798A (talk) 14:37, 5 April 2019 (UTC)