| Frucht graph | |
|---|---|
 The Frucht graph | |
| Named after | Robert Frucht |
| Vertices | 12 |
| Edges | 18 |
| Radius | 3 |
| Diameter | 4 |
| Girth | 3 |
| Automorphisms | 1 ({id}) |
| Chromatic number | 3 |
| Chromatic index | 3 |
| Properties | Cubic Halin Pancyclic |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries.[1] It was first described by Robert Frucht in 1939.[2]
The Frucht graph is a pancyclic, Halin graph with chromatic number 3, chromatic index 3, radius 3, and diameter 4. Like every Halin graph, the Frucht graph is polyhedral (planar and 3-vertex-connected) and Hamiltonian, with girth 3. Its independence number is 5.
The Frucht graph can be constructed from the LCF notation: [−5,−2,−4,2,5,−2,2,5,−2,−5,4,2].
- ^ Weisstein, Eric W., "Frucht Graph", MathWorld
- ^ Cite error: The named reference
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