High Quality Content by WIKIPEDIA articles! In the mathematical field of graph theory, the Tutte 12-cage or Benson graph is a 3-regular graph with 126 vertices and 189 edges named after W. T. Tutte. The Tutte 12-cage is the unique (3-12)-cage. It was discovered by C. T. Benson in 1966. It has chromatic number 2 (bipartite), chromatic index 3, girth 12 (as a 12-cage) and diameter 6. Its crossing number is 170 and has been conjectured to be the smallest cubic graph with this crossing number.

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