G127

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G127 is a graph on 127 vertices, numbered 0 through 126, with 2667 edges, an edge is placed between two vertices that satisfy the following.

  • j, i are vertex numbers.
  • j - i = a3, 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.[1]

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