Noncayley Graph

Author

Eric W. Weisstein
February 10, 2011

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

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

©2011 Wolfram Research, Inc. except for portions noted otherwise

VT Noncayley

Counts

vtnc={0,0,0,0,0,0,0,0,0,2,0,0,0,0,4,8,0,4,0,82,0,0,0,112,0,132,0,66,0,1124,0};

Table[GraphData[{"VertexTransitive","Noncayley"},n],{n,18}]

Grid[
Table[{n,vtnc[[n]],GraphData[{"VertexTransitive","Noncayley"},n]//Length},
{n,Length[vtnc]}],
Dividers->All,Alignment->Decimal
]//TraditionalForm

Partition[vtn,2,2,1,{}][[All,1]]

Table

Cases[GraphData[{"VertexTransitive","Noncayley"}],{"NoncayleyTransitiveGraph",_}]

Grid[Sort[
Most/@DeleteCases[GraphData[{"VertexTransitive","Noncayley"},{"V","Name","#"}],{_,_,{"NoncayleyTransitiveGraph",_}}]
],Dividers->All,Alignment->{{Decimal,Left},Automatic}]//TraditionalForm

Figure

Original

GraphicsGrid[Map[Show[GraphData[#,"Image"],PlotLabel->TextCell[Style[GraphData[#,"Name"],Italic],PageWidth->100,TextAlignment->Center]]&,DeleteCases[Table[DeleteCases[GraphData[{"VertexTransitive","Noncayley"},n],{"NoncayleyTransitiveGraph",_}],{n,24}],{}],{2}],ImageSize->400,Spacings->{-30,Automatic}]

New

GraphicsGrid[Map[Show[GraphData[#,"Image"],PlotLabel->TextCell[Style[GraphData[#,"Name"],Italic],PageWidth->100,TextAlignment->Center]]&,
Flatten[Partition[#,4,4,{1,1},{}]&/@DeleteCases[Table[GraphData[{"VertexTransitive","Noncayley"},n],{n,19}],{}],1],
{2}],ImageSize->400,Spacings->{-30,Automatic}]

GraphData

SetDirectory[$dir="/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Royle/Noncayley/"];

files=Most[Complement[FileNames["*.g6"],FileNames["*c.g6"]]]

Length[gs=Select[Flatten[Function[f,MapIndexed[{{VertexCount[#],#2[[1]]},#}&,Import[f]]]/@files,1],RecognizeGraph[#[[2]]]==={}&]]

gs[[All,1]]

Position[gs,{26,125}]