Tutte–Coxeter graph
In the mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth 8, it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle W2 (known as the Cremona–Richmond configuration). The graph is named after William Thomas Tutte and H. S. M. Coxeter; it was discovered by Tutte (1947) but its connection to geometric configurations was investigated by both authors in a pair of jointly published papers (Tutte 1958; Coxeter 1958a).
| Tutte–Coxeter graph | |
|---|---|
| Named after | W. T. Tutte H. S. M. Coxeter |
| Vertices | 30 |
| Edges | 45 |
| Radius | 4 |
| Diameter | 4 |
| Girth | 8 |
| Automorphisms | 1440 (Aut(S6)) |
| Chromatic number | 2 |
| Chromatic index | 3 |
| Book thickness | 3 |
| Queue number | 2 |
| Properties | Cubic Cage Moore graph Symmetric Distance-regular Distance-transitive Bipartite |
| Table of graphs and parameters | |
All the cubic distance-regular graphs are known. The Tutte–Coxeter is one of the 13 such graphs.
It has crossing number 13, book thickness 3 and queue number 2.