Wagner Graph

Author

Eric W. Weisstein
August 23, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/WagnerGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WagnerGraph.html.

©2022 Wolfram Research, Inc. except for portions noted otherwise

Embeddings

GraphData["WagnerGraph","StandardName"]

GraphData["WagnerGraph","AlternateStandardNames"]

Default

GraphData["WagnerGraph"]//StyleGraphs[#,ImageSize->Small]&

Read and Wilson

All

GraphData["WagnerGraph","Graph","All"]//StyleGraphs

Circulant

GraphData["WagnerGraph","Graph","Circulant"]//StyleGraphs

Halin

GraphData["WagnerGraph","Halin"]

GraphData["WagnerGraph","Graph","Halin"]//StyleGraphs

LCF

GraphData["WagnerGraph","LCF"]

GraphData["WagnerGraph","LCFSignature"]

GraphData["WagnerGraph","Graph","LCF"]//StyleGraphs

UnitDistance

GraphData["WagnerGraph","UnitDistance"]

UnitDistanceGraphQ[GraphData["WagnerGraph"],Debug->True]//Timing

GraphData["WagnerGraph","Graph","UnitDistance"]//StyleGraphs

Matchstick

GraphData["WagnerGraph","Matchstick"]

GraphData["WagnerGraph","Graph","Matchstick"]//StyleGraphs

MinimalCrossing

GraphData["WagnerGraph",{"RCN","CN"}]

GraphData["WagnerGraph","Graph","MinimalCrossing"]//StyleGraphs

Default embedding

GraphPlot@GraphData["WagnerGraph","Edges"]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

MinimalCrossing construction

GraphPlot@RotateGraph[MinimalCrossingGraph[GraphData["WagnerGraph"],"CrossingNumber"->1],-.95-Pi/2]

v={{0,0},{1,0},{0,1},{1/4,1},{1/2,1},{3/4,1},{1,1},{1/2,1+Sqrt[3]/2}};
g=Graph[Range[Length[v]],UndirectedEdge@@@{e[1,2,7,6,5,4,3,1,6],e[3,8,7],{5,8},{2,4}},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

RectilinearCrossingCount[g]

3D default

Graph3D[GraphData["WagnerGraph","Edges"]]

3D All

GraphData["WagnerGraph","Graph",{"3D","All"}]

3D UnitDistance

GraphData["WagnerGraph","Graph",{"3D","UnitDistance"}]

3D Polyhedron

GraphData["WagnerGraph","Polyhedral"]

GraphData["WagnerGraph","Graph",{"3D","Polyhedron"}]