Polyhedral Graph

Author

Eric W. Weisstein
October 12, 2022

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

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

©2022 Wolfram Research, Inc. except for portions noted otherwise

Enumeration by VertexCount

A000944

0, 0, 0, 1, 2, 7, 34, 257, 2606, 32300, 440564, 6384634, 96262938, 1496225352, 23833988129, 387591510244, 6415851530241, 107854282197058

PolyhedralGraphs

Length/@PolyhedralGraphs/@Range[9]//Timing

PolyhedralGraphQ

Count[#,_?PolyhedralGraphQ]&/@Graphs/@Range[8]//Timing

Count[#,_?PolyhedralGraphQ]&/@PlanarConnectedGraphs/@Range[8]//Timing

GraphData

Length/@Table[GraphData["Polyhedral",n],{n,9}]

plantri

Length/@Table[PolyhedralGraphs[n],{n,10}]//Timing

Do[Print[{n,Length@PolyhedralGraphs[n]//Timing}],{n,11}]

~/src/plantri52/plantri -p -s 13 Polyhedral_13.s6
96262938 polytopes written to Polyhedral_13.s6; cpu=199.83 sec

mkdir 13
cd 13
split -l 10000000 -a 3 --numeric-suffixes=1 ../Polyhedral_13.s6 p

$ ls -lh
total 2.4G
-rw-r--r-- 1 eww users 252M May  4 08:36 p001
-rw-r--r-- 1 eww users 252M May  4 08:36 p002
-rw-r--r-- 1 eww users 248M May  4 08:36 p003
-rw-r--r-- 1 eww users 251M May  4 08:36 p004
-rw-r--r-- 1 eww users 254M May  4 08:36 p005
-rw-r--r-- 1 eww users 255M May  4 08:36 p006
-rw-r--r-- 1 eww users 250M May  4 08:36 p007
-rw-r--r-- 1 eww users 252M May  4 08:36 p008
-rw-r--r-- 1 eww users 253M May  4 08:36 p009
-rw-r--r-- 1 eww users 160M May  4 08:36 p010

Write to File

Put[Select[PlanarConnectedGraphs[9],KConnectedQ[3,#]&],"PolyhedralGraphs9.m"]//Timing

Enumeration by EdgeCount

{0,0,0,0,0,1,0,1,2,2,4,12,22,58,158,448,1342,4199,13384,43708,144810,485704}

Graphics

GraphicsGrid[Flatten[Partition[#,UpTo[4]]&/@Map[Show[StyleGraphs[GraphData[#],VertexSize->{"Scaled",.03}],PlotLabel->TextCell[GraphData[#,"Name"],TextAlignment->Center,PageWidth->140],LabelStyle->Directive[12,Black,Italic,FontFamily->"Times"]]&,GraphData["Polyhedral",#]&/@Range[4,6],{2}],1],ImageSize->600,Dividers->{{Thick,{True},Thick},{{Thick},True,Thick}}]