Tripod

Author

Eric W. Weisstein
May 16, 2017

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

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

©2017 Wolfram Research, Inc. except for portions noted otherwise

Counts

A001399

Table[Total[Boole[TripodGraphQ/@Trees[n]]],{n,16}]//Timing

Table[Length@GraphData["Tripod",n],{n,10}]

Table[Count[Trees[n],_?(Count[VertexDegree[#],1]===3&)],{n,20}]//Timing

Image

l=#[[All,2]]&/@{{{4,"ClawGraph"}},{{5,"ForkGraph"}},{{6,"EGraph"},{6,{"Tree",{6,2}}}},{{7,{"Tree",{7,7}}},{7,{"Tree",{7,8}}},{7,{"Tree",{7,9}}}},{{8,{"Tree",{8,2}}},{8,{"Tree",{8,3}}},{8,{"Tree",{8,5}}},{8,{"Tree",{8,7}}}},{{9,{"Firecracker",{3,3}}},{9,{"Tree",{9,2}}},{9,{"Tree",{9,3}}},{9,{"Tree",{9,5}}},{9,{"Tree",{9,7}}}}};

GraphicsGrid[Map[Show[GraphData[#,"Image"],PlotLabel->TextCell[Style[GraphData[#,"Name"],Italic],PageWidth->80,TextAlignment->Center]]&,l,{2}],ImageSize->400]

Ennumeration

t=Select[GraphData["Tree"],Count[GraphData[#,"Degrees"],1]===3&]

SortBy[GraphData[#,{"V","#"}]&/@t,First]

SplitBy[%,First]

Length/@%

Checks

DeleteCases[{#,GraphData[#,"Tripod"],TreeGraphQ[GraphData[#]]&&Count[VertexDegree[GraphData[#]],1]===3}&/@GraphData[All],{_,x_,x_}]//Timing

DeleteCases[{#,GraphData[#,"Tripod"],Count[VertexDegree[GraphData[#]],1]===3&&TreeGraphQ[GraphData[#]]}&/@GraphData[All],{_,x_,x_}]//Timing