Cycle Complement Graph

Author

Eric W. Weisstein
February 2, 2021

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

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

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

Figures

<<MathWorld`Graphs`

GraphicsRow[g1=Table[Show[GraphComplement[CycleGraph[n]]//StyleGraphs[#,VertexSize->{"Scaled",.05}]&,PlotLabel->Column[{Row[{Style["n",Italic]," == ",n}]},BaseStyle->Directive[Black,FontFamily->"Times"]]],{n,3,7}]]

GraphicsRow[g2=Table[Show[GraphData[{"CycleComplement",n}]//StyleGraphs[#,VertexSize->{"Scaled",.05}]&,PlotLabel->Column[{Row[{Style["n",Italic]," == ",n}]},BaseStyle->Directive[Black,FontFamily->"Times"]]],{n,3,7}]]

GraphicsGrid[{g1,g2},Dividers->All]

Special cases

TextGrid[Table[{n,r=RecognizeGraph@GraphComplement[CycleGraph[n]],"Circulant"/.GraphData[r,"NotationRules"],{n,Piecewise[{{{2},n==4},{Join[Range[n/2-2],Range[n/2-1,n/2]],Mod[n,2]==0},{XXX,Mod[n,2]==1}}]}},{n,3,20}],Dividers->All]

GraphData

GraphDataString

file=OpenWrite["~/cycle-complement.m"]

Do[WriteString[file,GraphDataString[GraphComplement[MyCycleGraph[n]],
"StandardName"->{"CycleComplement",n},
"Name"->IntegerString[n]<>"\[Hyphen]cycle complement graph",
"Classes"->{"CycleComplement"},
"NotationRules"->{"CycleComplement"->n},
"Skip"->{"Arboricity","CliqueCoveringNumber","ConnectedDominatingSets","ConstructionNumber",,"Minors","TuttePolynomial"},
TimeConstraint->10,
Debug->True
]],{n,11,20}];

Close[file]