FruchtGraph - Maple Help

GraphTheory[SpecialGraphs]

 FruchtGraph
 construct Frucht graph

 Calling Sequence FruchtGraph()

Description

 • The FruchtGraph() command constructs the Frucht graph.
 • The Frucht graph is a 3-regular graph with 12 vertices and 18 edges and no nontrivial automorphisms. It was first described by Robert Frucht in 1939.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $F≔\mathrm{FruchtGraph}\left(\right)$
 ${F}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 12 vertices and 18 edge\left(s\right)}}$ (1)
 > $\mathrm{ChromaticNumber}\left(F\right)$
 ${3}$ (2)

The Frucht graph has no nontrivial automorphisms.

 > $\mathrm{Aut}≔\mathrm{AutomorphismGroup}\left(F\right)$
 ${\mathrm{Aut}}{≔}⟨⟩$ (3)
 > $\mathrm{GroupTheory}:-\mathrm{GroupOrder}\left(\mathrm{Aut}\right)$
 ${1}$ (4)
 > $\mathrm{DrawGraph}\left(F\right)$

References

 "Frucht graph", Wikipedia. http://en.wikipedia.org/wiki/Frucht_graph

Compatibility

 • The GraphTheory[SpecialGraphs][FruchtGraph] command was introduced in Maple 2017.