Singlecross Graph

Author

Eric W. Weisstein
February 10, 2021

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

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

©2021 Wolfram Research, Inc. except for portions noted otherwise

Counts

All

A307071

Compute

Table[Total[Boole[AlmostPlanarGraphQ/@Graphs[n]]],{n,8}]//Timing

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Nodes/AlmostPlanar"];

tallies=Count[Get[#],True]&/@FileNames["*.m"]

QuickCross: (agrees between 100 and 200 iterations)

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Nodes/CrossingNumber"];

tallies=Count[Get[#],1]&/@FileNames["*.m"]

Exoo: [wrong for at least 9 connected graphs listed as RCN = 2 but actually = 1]

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Nodes/RectilinearCrossingNumber"];

tallies=Count[Get[#],1]&/@FileNames["*.m"]

GraphData:

Length/@Table[Select[GraphData[n],GraphData[#,"RCN"]==1&],{n,7}]

Connected

A307072

Compute

Table[Total[Boole[AlmostPlanarGraphQ/@ConnectedGraphs[n]]],{n,8}]//Timing

tallies=Count[Get[#][[ConnectedGraphIndices[FromDigits[StringReplace[StringCases[#,NumberString][[1]],"."->""]]]]],True]&/@FileNames["*.m"]

QuickCross: (agrees between 100 and 200 iterations)

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Nodes/CrossingNumber"];

tallies=Count[Get[#][[ConnectedGraphIndices[FromDigits[StringTake[StringCases[#,NumberString][[1]],{2,-2}]]]]],1]&/@FileNames["*.m"]

Exoo: [wrong for at least 9 connected graphs listed as RCN = 2 but actually = 1]

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Nodes/RectilinearCrossingNumber"];

tallies=Count[Get[#][[ConnectedGraphIndices[FromDigits[StringTake[StringCases[#,NumberString][[1]],{2,-2}]]]]],1]&/@FileNames["*.m"]

GraphData:

Length/@Table[Select[GraphData["Connected",n],GraphData[#,"RCN"]==1&],{n,7}]

Graphics

All

GraphicsGrid[Map[Show[StyleGraphs[GraphData[#,"Graph","MinimalRectilinearCrossing"][[1]],VertexSize->Scaled[.1]],PlotLabel->TextCell[Style[GraphData[#,"Name"],Black,FontFamily->"Times",Italic],PageWidth->100,TextAlignment->Center]]&,Flatten[Partition[#,UpTo[5]]&/@Table[Select[GraphData[n],GraphData[#,"RCN"]==1&],{n,6}],1],{2}],Dividers->All,ImageSize->500]

Connected

GraphicsGrid[Map[Show[StyleGraphs[GraphData[#,"Graph","MinimalRectilinearCrossing"][[1]],VertexSize->Scaled[.1]],PlotLabel->TextCell[Style[GraphData[#,"Name"],Black,FontFamily->"Times",Italic],PageWidth->100,TextAlignment->Center]]&,Flatten[Partition[#,UpTo[5]]&/@Table[Select[GraphData["Connected",n],GraphData[#,"RCN"]==1&],{n,6}],1],{2}],Dividers->All,ImageSize->500]

Classes that are Singlecross

GraphClassesThatAreClass["Singlecross"]