Quartic Symmetric Graph

Author

Eric W. Weisstein
December 9, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

V5

Length/@(symquart=Table[Select[Graphs[n],QuarticQ[#]&&SymmetricGraphQ[#]&],{n,9}])//Timing

ShowGraphArray[RecognizeGraph/@Flatten[symquart],AspectRatio->Automatic]

PolyhedralQ/@Flatten[symquart]

PlanarQ/@Flatten[symquart]

ConnectedQ/@Flatten[symquart]

V7

l=SortBy[GraphData[{"Quartic","Symmetric","Connected"}],GraphData[#,"V"]&]

Length[l]

(#[[1,1]]->#[[All,2]])&/@SplitBy[GraphData[#,{"V","#"}]&/@l,First]//Column

GraphicsGrid[Partition[Show[GraphData[#],PlotLabel->TextCell[GraphData[#,"Name"],PageWidth->70,TextAlignment->Center],BaseStyle->{Italic,FontSize->9}]&/@Drop[l,-3],5,5,{1,1},{}]/.AbsolutePointSize[_]:>AbsolutePointSize[4],ImageSize->400]