Antipodal Graph

Author

Eric W. Weisstein
November 29, 2021

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

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

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

Code

GraphDistanceMatrix[CycleGraph[5]]

GraphDistanceMatrix[CycleGraph[6]]

AllTrue[%,Count[#,Max[#]]===1&]

GraphDistanceMatrix[GraphData["K4+K1"]]

Figure

gs=DeleteCases[Table[GraphData["Antipodal",n],{n,6}],{}];

i=0;
GraphicsGrid[Map[Annotate[StyleGraphs[#,VertexSize->If[++i==1,.015,{"Scaled",.06}]]&@GraphData[#],{PlotLabel->TextCell[GraphData[#,"Name"],PageWidth->100],LabelStyle->Directive[Black,Italic,FontFamily->"Times"]}]&,gs,{2}],Dividers->All,ImageSize->500,Alignment->Center]

7

GraphData["Antipodal",7]

Annotate[GraphData[#],ImageSize->Tiny]&/@GraphData["Antipodal",7]//StyleGraphs

8

GraphData["Antipodal",8]

Annotate[GraphData[#],ImageSize->Tiny]&/@GraphData["Antipodal",8]//StyleGraphs

Counts

Table[Select[GraphData[i],AntipodalGraphQ[GraphData[#]]&],{i,4}]

Connected (same as All since connected by definition)

A349635

Table[Total[Boole[AntipodalGraphQ/@ConnectedGraphs[n]]],{n,10}]//Timing

Length/@Table[GraphData["Antipodal",n],{n,10}]

Classes

Intersection@@GraphData["Antipodal","Classes"]

GraphClassesThatAreClass["Antipodal"]

Do[Print[{n,AntipodalGraphQ[BruhatGraph[n]]//Timing}],{n,8}]

Compute

(data=Monitor[{g=#,TimeConstrained[AntipodalGraphQ[GraphData[#]],10]//Timing}&/@GraphData[All],g])//Timing

Cases[data,{g_,{_,$Aborted}}:>g]

Cases[data,{g_,{_,True}}:>g]

l=DeleteCases[data,{_,{_,$Aborted}}]

MissingFillin[l,"Antipodal","13.1"]

RenameGraphFiles[]