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Frucht graph
Cubic graph with 12 vertices and 18 edges / From Wikipedia, the free encyclopedia
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]
Quick Facts Named after, Vertices ...
Frucht graph | |
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![]() 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 |
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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].