Tutte 12-cage
| Tutte 12-cage | |
|---|---|
The Tutte 12-cage | |
| Named after | W. T. Tutte |
| Vertices | 126 |
| Edges | 189 |
| Radius | 6 |
| Diameter | 6 |
| Girth | 12 |
| Automorphisms | 12096 |
| Chromatic number | 2 |
| Chromatic index | 3 |
| Genus | 17 |
| Properties | Cubic Cage Hamiltonian Semi-symmetric Bipartite |
| Table of graphs and parameters | |
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. It is named after W. T. Tutte.
The Tutte 12-cage is the unique (3-12)-cage (sequence A052453 in the OEIS). 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 known to be less than 165, see Wolfram MathWorld.