graphscope.nx.generators.small.frucht_graph

graphscope.nx.generators.small.frucht_graph(create_using=None)

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_using (NetworkX graph constructor, optional (default=nx.Graph)) – Graph type to create. If graph instance, then cleared before populated.

Returns:

G – Frucht Graph with 12 nodes and 18 edges

Return type:

networkx Graph

References

[1]

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

[2]

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