G127

G127

G127 is a graph on 127 vertices, identified with the numbers 0 through 126, with 2667 edges, in which an edge is placed between two vertices "i", "j", whenever "j" − "i" = "a"3, meaning "j" − "i" is a cubic residue.

G127 is a 42-regular graph, not containing any four-vertex clique. It was studied by Jonathan Cole and C.P. Knerr with the aim of proving that every partition of its edges into two subgraphs must have a triangle in one or the other of the subgraphs. [http://www.cs.rit.edu/~cpk8576/FolkmanPresentation/text0.html]

ee also

*Ramsey's theorem


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