IsArchimedeanGraph - Maple Help

GraphTheory

 IsArchimedeanGraph
 test if graph is Archimedean

 Calling Sequence IsArchimedeanGraph(G)

Parameters

 G - graph

Description

 • IsArchimedeanGraph(G) returns true if G is an Archimedean graph and false otherwise.

Definition

 • An Archimedean graph is a graph that forms the graph skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all of them are regular, polyhedral, planar, and Hamiltonian.

List of Archimedean graphs

 Name Degree Vertices Edges Order 3 12 18 24 4 12 24 48 3 24 36 48 3 24 36 48 4 24 48 48 3 48 72 48 5 24 60 24 4 30 60 120 3 60 90 120 3 60 90 120 4 60 120 120 3 120 180 120 5 60 150 60

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{SB}≔\mathrm{SoccerBallGraph}\left(\right)$
 ${\mathrm{SB}}{≔}{\mathrm{Graph 1: an undirected graph with 60 vertices and 90 edge\left(s\right)}}$ (1)
 > $\mathrm{IsPlanar}\left(\mathrm{SB},'F'\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{nops}\left(F\right)$
 ${32}$ (3)
 > $\mathrm{IsArchimedeanGraph}\left(\mathrm{SB}\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{DrawGraph}\left(\mathrm{SB},\mathrm{style}=\mathrm{spring}\right)$
 > $\mathrm{DrawGraph}\left(\mathrm{SB},\mathrm{style}=\mathrm{spring},\mathrm{dimension}=3\right)$

Compatibility

 • The GraphTheory[IsArchimedeanGraph] command was introduced in Maple 2024.