Balaban 11-Cage

Author

Eric W. Weisstein
May 16, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/Balaban11-Cage.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Balaban11-Cage.html.

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

Embeddings

GraphData["Balaban11Cage","StandardName"]

All

GraphData["Balaban11Cage","Graph","All"]//StyleGraphs

Halin

GraphData["Balaban11Cage","Graph","Halin"]//StyleGraphs

LCF

GraphData["Balaban11Cage","LCFSignature"]

GraphData["Balaban11Cage","Graph","LCF"]//StyleGraphs

UnitDistance

GraphData["Balaban11Cage","UnitDistance"]

UnitDistanceGraphQ[GraphData["Balaban11Cage"],Debug->True]//Timing

GraphData["Balaban11Cage","Graph","UnitDistance"]//StyleGraphs

Select[%,!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&]

Select[UnitDistanceEmbeddingRefine/@Complement@@(GraphData["Balaban11Cage","Graph",#]&/@{"All","UnitDistance"}),UnitDistanceGraphEmbeddingQ]

FindUnitDistanceEmbedding[GraphData["Balaban11Cage"],MaxIterations->5000,"ReturnWithMessage"->True]//Timing

UnitDistance FindSubgraphUnitDistanceEmbedding

{"Balaban11Cage",l=FindSubgraphUnitDistanceEmbedding[GraphData["Balaban11Cage"],TimeConstraint->300,"Results"->All]//Timing}

gs=UniqueEmbeddings[l]

Matchstick

GraphData["Balaban11Cage","Graph","Matchstick"]//StyleGraphs

MinimalCrossing

GraphData["Balaban11Cage",{"RCN","CN"}]

GraphData["Balaban11Cage","Graph","MinimalCrossing"]//StyleGraphs

Default embedding

g=Graph@GraphData["Balaban11Cage","Edges"]

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

RecognizeGraph[g]

MinimalCrossing Construction

GraphPlot@RotateGraph[MinimalCrossingGraph[GraphData["Balaban11Cage"]]]

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

RecognizeGraph[g]

RectilinearCrossingCount[g]

3D default

Graph3D[GraphData["Balaban11Cage","Edges"]]

3D All

GraphData["Balaban11Cage","Graph",{"3D","All"}]

Matrices

GraphDataMatrices["Balaban11Cage"]

Properties

GraphData["Balaban11Cage",{"VertexCount","EdgeCount"}]

GraphData["Balaban11Cage","Classes"]

(#->GraphData["Balaban11Cage",#])&/@GraphData["Properties"]//ColumnForm

GraphData

GraphClassString

GraphClassString["Balaban11Cage"]