Frucht graph
| Frucht graph | |
|---|---|
 The Frucht graph | |
| Named after | Robert Frucht |
| Vertices | 12 |
| Edges | 18 |
| Radius | 3 |
| Diameter | 4 |
| Girth | 3 |
| Automorphisms | identity |
| Chromatic number | 3 |
| Chromatic index | 3 |
| Properties | Cubic Halin Pancyclic |
| Table of graphs and parameters | |
In graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in 1949.
The Frucht graph can be constructed from the LCF notation: [−5,−2,−4,2,5,−2,2,5,−2,−5,4,2]. This describes it as a cubic graph in which two of the three adjacencies of each vertex form part of a Hamiltonian cycle and the numbers specify how far along the cycle to find the third neighbor of each vertex.