networkx.generators.small.frucht_graph

frucht_graph(create_using=None)[source]

Returns the Frucht Graph.

The Frucht Graph is the smallest cubical graph whose automorphism group consists only of the identity element [1]. It has 12 nodes and 18 edges and no nontrivial symmetries. It is planar and Hamiltonian [2].

Parameters
create_usingNetworkX graph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated.

Returns
Gnetworkx Graph

Frucht Graph with 12 nodes and 18 edges

References

1

https://en.wikipedia.org/wiki/Frucht_graph

2

https://mathworld.wolfram.com/FruchtGraph.html