| 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[1] is a 3-regular graph with 126 vertices and 189 edges. It is named after W. T. Tutte.[2]
The Tutte 12-cage is the unique (3-12)-cage (sequence A052453 in the OEIS). It was discovered by C. T. Benson in 1966.[3] 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.[4][5]
- ^ Cite error: The named reference
SURVwas invoked but never defined (see the help page). - ^ Weisstein, Eric W. "Tutte 12-cage". MathWorld.
- ^ Benson, C. T. "Minimal Regular Graphs of Girth 8 and 12." Can. J. Math. 18, 1091–1094, 1966.
- ^ Exoo, G. "Rectilinear Drawings of Famous Graphs".
- ^ Pegg, E. T. and Exoo, G. "Crossing Number Graphs." Mathematica J. 11, 2009.