Pseudotree

Author

Eric W. Weisstein
June 11, 2012

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

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

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

Counts

A005703

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

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

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

Disconnected

0 by definition

Table[Total[Boole[Get[FileNameJoin[{$GraphDataDirectory,"Nodes","Pseudotree","Pseudotree_"<>If[n<10,"0",""]<>ToString[n]<>".m"}]][[DisconnectedGraphIndices[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,-2],{2}],1],ImageSize->500,Dividers->{All,{True,Thick,Thick,Thick,Thick,True,True}}]

Checks

l=Monitor[{Print[#];g=#,GraphData[#,"Pseudotree"],TimeConstrained[PseudotreeQ[GraphData[#]],1]}&/@Drop[GraphData[All],0],g];//Timing

lattice 10,10

m22graph

kneser 13,5

McLaughlinGaph

Lattice 8,8

Position[GraphData[All],"McLaughlinGraph"]

Hypbercube,10