Pseudoforest

Author

Eric W. Weisstein
June 11, 2012

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

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

©2012 Wolfram Research, Inc. except for portions noted otherwise

Counts

A134964

Total[Boole[Get[#]]]&/@FileNames["*.m",FileNameJoin[{$GraphDataDirectory,"Nodes","Pseudoforest"}]]

Length/@(c=Table[Select[GraphData[n],PseudoforestQ[GraphData[#]]&],{n,7}])//Timing

Do[Print[{n,Count[Graphs[n],_?PseudoforestQ]//Timing}],{n,10}]

Connected

=== Pseudotree

A005703

Table[Total[Boole[Get[FileNameJoin[{$GraphDataDirectory,"Nodes","Pseudoforest","Pseudoforest_"<>If[n<10,"0",""]<>ToString[n]<>".m"}]][[ConnectedGraphIndices[n]]]]],{n,10}]

Graphic

GraphicsGrid[Flatten[Partition[#,5,5,1,{}]&/@Map[Show[GraphData[#,"Image"],PlotLabel->TextCell[Style[GraphData[#,"Name"],Italic],PageWidth->80,TextAlignment->Center]]&,Drop[c,-3],{2}],1],ImageSize->500,Dividers->{All,{True,Thick,Thick,Thick,True,True}}]

Examples

Show[GraphData[{7,23}],ImageSize->Small]

All

pf=GraphData["Pseudoforest"]

Show[GraphData[#],PlotLabel->#]&/@pf