Nuciferous Graph

Author

Eric W. Weisstein
October 28, 2023

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

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

©2023 Wolfram Research, Inc. except for portions noted otherwise

Counts

All

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

Length/@Table[Select[Graphs[n],NuciferousGraphQ],{n,8}]//Timing

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

ToEntity/@Select[Flatten[Table[Graphs[n],{n,5}]],NuciferousGraphQ]

Table[Total[Boole[NuciferousGraphQ/@Graphs[n]]],{n,8}]//Timing

Table[Total[Boole[NuciferousGraphQ/@Graphs[n]]],{n,10}]//Timing

Table[Length@GraphData["Nuciferous",n],{n,12}]

Only nuciferous graph on ≤ 10 nodes is (Subscript[P, 2])

Connected

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

Table[Total[Boole[NuciferousGraphQ/@ConnectedGraphs[n]]],{n,10}]//Timing

Table[Length@GraphData[{"Connected","Nuciferous"},n],{n,12}]

GraphData |V| ≤ 1000

Monitor[Select[GraphData[;;1000],NuciferousGraphQ[GraphData[g=#]]&],g]//Timing

VertexTransitive

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Royle/VertexTransitive/"];

files=FileNames["trans"~~NumberString~~".g6"]

Print[{#,Length[gs=Import[#]],Flatten[Position[gs,_?NuciferousGraphQ]]//Timing}]&/@files;

Length[{8077,23514,23612,23902,24388,24393,25409,25824,26697,27267,27814,45788}]

Import["trans30.g6",{"GraphList",{8077,23514,23612,23902,24388,24393,25409,25824,26697,27267,27814,45788}}]

RecognizeGraph/@%

GraphData[#,"Nuciferous"]&/@%

Noncayley

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Royle/Noncayley/"];

files=FileNames["noncay"~~NumberString~~".g6"]

Print[{#,Length[gs=Import[#]],Flatten[Position[gs,_?NuciferousGraphQ]]//Timing}]&/@files;

Cayley

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Royle/Cayley/"];

files=FileNames["cay"~~NumberString~~".g6"]

Print[{#,Length[gs=Import[#]],Flatten[Position[gs,_?NuciferousGraphQ]]//Timing}]&/@files;

Definition

Let G be a simple graph with non-singular 0-1 adjacency matrix A. If all the diagonal entries of A−1 are zero and all the off-diagonal entries of A−1 are non-zero, then G is called a nuciferous graph.

Embeddings

<<MathWorld`Graphs`

GraphData["Nuciferous*"]

{"Nuciferous", {24, 1}}

Names

GraphData[{"Nuciferous",{24,1}},"StandardName"]

GraphData[{"Nuciferous",{24,1}},"StandardNames"]

Primary

GraphData[{"Nuciferous",{24,1}}]//StyleGraphs[#,ImageSize->Small]&

All

GraphData[{"Nuciferous",{24,1}},"Graph","All"]//StyleGraphs

Inexact

Select[GraphData[{"Nuciferous",{24,1}},"Graph","All"],(!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&)]//StyleGraphs

Embedding types

GraphDataEmbeddings[GraphData[{"Nuciferous",{24,1}},"EdgeList"]]

Default embedding

GraphPlot@GraphData[{"Nuciferous",{24,1}},"Edges"]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

Degenerate

GraphData[{"Nuciferous",{24,1}},"Graph","Degenerate"]//StyleGraphs

DegenerateGraphEmbeddingTypes/@GraphData[{"Nuciferous",{24,1}},"Graph","Degenerate"]

Perspective

GraphData[{"Nuciferous",{24,1}},"Graph","Perspective"]//StyleGraphs

Perspective construction

GraphData[{"Nuciferous",{24,1}},"Polyhedron"]

Bilateral

GraphData[{"Nuciferous",{24,1}},"Graph","Bilateral"]//StyleGraphs

Circular

GraphData[{"Nuciferous",{24,1}},"Graph","Circular"]//StyleGraphs

Planar

GraphData[{"Nuciferous",{24,1}},"Planar"]

GraphData[{"Nuciferous",{24,1}},"Graph","Planar"]//StyleGraphs

MinimalCrossing

GraphData[{"Nuciferous",{24,1}},{"RCN","CN"}]

GraphData[{"Nuciferous",{24,1}},"Graph","MinimalCrossing"]//StyleGraphs

MinimalCrossing construction

(cn=CrossingNumber[GraphData[{"Nuciferous",{24,1}}],TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData[{"Nuciferous",{24,1}}],TimeConstraint->10])//AbsoluteTiming

(g=MinimalCrossingGraph[GraphData[{"Nuciferous",{24,1}}],"CrossingNumber"->cn])//PolyhedralGraphQ

faces=ReverseSort@SymmetricallyDistinctFaces[g]

Tally[ReverseSort[Length/@faces]]

IGLayoutTutte[g,"OuterFace"->#]&/@faces

Union[Select[Table[RotateGraph[MinimalCrossingGraph[GraphData[{"Nuciferous",{24,1}}],"CrossingNumber"->cn,RandomSeed->n]],{n,50}],Max[OuterFace[#]]<=GraphData[{"Nuciferous",{24,1}},"V"]&]]//Timing

Table[MinimalCrossingGraph[GraphData[{"Nuciferous",{24,1}}],"CrossingNumber"->cn,RandomSeed->i],{i,50}]//Union

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

RectilinearCrossingCount[g]

Circulant

GraphData[{"Nuciferous",{24,1}},"Circulant"]

GraphData[{"Nuciferous",{24,1}},"Graph","Circulant"]//StyleGraphs

Complement graph

GraphData[{"Nuciferous",{24,1}},"ComplementGraph","Name"]

Line graph

GraphData[{"Nuciferous",{24,1}},"Line"]

LineGraphQ[GraphData[{"Nuciferous",{24,1}}]]//Timing

RootGraph

Select[GraphData[All],GraphData[#,"LineGraph","Name"]=== {"Nuciferous",{24,1}}&]

RootGraph[GraphData[{"Nuciferous",{24,1}}]]

Halin

GraphData[{"Nuciferous",{24,1}},"Halin"]

GraphData[{"Nuciferous",{24,1}},"Graph","Halin"]//StyleGraphs

Rigid

GraphData[{"Nuciferous",{24,1}},"Rigid"]

GraphData[{"Nuciferous",{24,1}},"Graph","Rigid"]//StyleGraphs

Flexible

GraphData[{"Nuciferous",{24,1}},"Flexible"]

GraphData[{"Nuciferous",{24,1}},"Graph","Flexible"]//StyleGraphs

LCF

GraphData[{"Nuciferous",{24,1}},"LCF"]

GraphData[{"Nuciferous",{24,1}},"HamiltonianCycleCount"]

GraphData[{"Nuciferous",{24,1}},"LCFSignature"]

GraphData[{"Nuciferous",{24,1}},"LCFNotations"]

GraphData[{"Nuciferous",{24,1}},"Graph","LCF"]//StyleGraphs

Tally[LCFNotation[#][[2]]&/@%]

LCF compute random

FindRandomLCFNotation[GraphData[{"Nuciferous",{24,1}}],TimeConstraint->120]

LCF compute 10^5

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,1}}],10^5])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs]

LCF compute 10^6

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,1}}],10^6])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1|2}]

LCFGraph@@@DeleteCases[lcf,{_,1|2}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,3])]//Timing

Length[gs]

gs

LCF compute 10^7

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,1}}],10^7])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1|2}]

LCFGraph@@@DeleteCases[lcf,{_,1|2}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,3])]//Timing

Length[gs]

gs

nicelcf={{{{-11,-9,-5,-3,9},{-11,-9,-2,6,10},{-6,-5,3,4,10},{-10,-8,-4,5,8},{-10,-7,-6,6,11},{-3,3,5,7,11},{-8,-4,6,8,11},{-11,-6,2,4,9}},3},{{{-11,-8,-6,4,8},{-11,-7,-5,-3,3},{-11,-6,6,7,10},{-8,-5,4,8,10},{-10,-4,-3,5,6},{-10,-6,2,9,11},{-9,3,5,9,11},{-9,-4,-2,6,11}},3}};

l={{{"Nuciferous",{24,1}},{0,Missing[nicelcf]}}}

PropertyReplace[l,"LCFNotations","14.1"]

RenameGraphFiles[]

LCF compute 5*^7

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,1}}],5*^7])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1|2}]

LCFGraph@@@DeleteCases[lcf,{_,1|2}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,3])]//Timing

Length[gs]

gs

LCF compute all

Length[FindHamiltonianCycle[GraphData[{"Nuciferous",{24,1}}],All][[All,All,1]]]//Timing

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,1}}],All])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

Tally[(lcf=ReadProperty["LCFNotations",GraphNameToFileName[{"Nuciferous",{24,1}},".m.gz"]])[[All,2]]]//Timing

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs]

gs

UnitDistance

GraphData[{"Nuciferous",{24,1}},"UnitDistance"]

UnitDistanceGraphQ[GraphData[{"Nuciferous",{24,1}}],Debug->True]//Timing

GraphData[{"Nuciferous",{24,1}},"Graph","UnitDistance"]//StyleGraphs

Select[%,!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&]

UnitDistance by refinement

UnitDistanceEmbeddingRefine[Graph[GraphData[{"Nuciferous",{24,1}},"VertexList"],GraphData[{"Nuciferous",{24,1}},"EdgeList"]],MaxIterations->500]

UnitDistanceGraphEmbeddingQ[%]

UnitDistanceEmbeddingRefine[Annotate[#,VertexCoordinates->N[GraphEmbedding[#]]],MaxIterations->500]&/@Complement@@(GraphData[{"Nuciferous",{24,1}},"Graph",#]&/@{"All","UnitDistance"})

Select[%,UnitDistanceGraphEmbeddingQ]

g=RotateGraph[,{22,18}]

UnitDistance by FindUnitDistanceEmbedding

FindUnitDistanceEmbedding[GraphData[{"Nuciferous",{24,1}}],MaxIterations->5000,"ReturnWithMessage"->True]//Timing

FindUnitDistanceEmbedding[GraphData[{"Nuciferous",{24,1}}],MaxIterations->5000,"ReturnWithMessage"->False]//Quiet//Timing

Matchstick

GraphData[{"Nuciferous",{24,1}},"Matchstick"]

GraphData[{"Nuciferous",{24,1}},"Graph","Matchstick"]//StyleGraphs

3D default

Graph3D[GraphData[{"Nuciferous",{24,1}},"Edges"]]

3D All

GraphData[{"Nuciferous",{24,1}},"Graph",{"3D","All"}]

3D UnitDistance

GraphData[{"Nuciferous",{24,1}},"Graph",{"3D","UnitDistance"}]

3D Polyhedron

GraphData[{"Nuciferous",{24,1}},"Polyhedral"]

GraphData[{"Nuciferous",{24,1}},"Graph",{"3D","Polyhedron"}]

{"Nuciferous", {24, 2}}

Names

GraphData[{"Nuciferous",{24,2}},"StandardName"]

GraphData[{"Nuciferous",{24,2}},"StandardNames"]

Primary

GraphData[{"Nuciferous",{24,2}}]//StyleGraphs[#,ImageSize->Small]&

All

GraphData[{"Nuciferous",{24,2}},"Graph","All"]//StyleGraphs

Inexact

Select[GraphData[{"Nuciferous",{24,2}},"Graph","All"],(!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&)]//StyleGraphs

Embedding types

GraphDataEmbeddings[GraphData[{"Nuciferous",{24,2}},"EdgeList"]]

Default embedding

GraphPlot@GraphData[{"Nuciferous",{24,2}},"Edges"]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

Degenerate

GraphData[{"Nuciferous",{24,2}},"Graph","Degenerate"]//StyleGraphs

DegenerateGraphEmbeddingTypes/@GraphData[{"Nuciferous",{24,2}},"Graph","Degenerate"]

Perspective

GraphData[{"Nuciferous",{24,2}},"Graph","Perspective"]//StyleGraphs

Perspective construction

GraphData[{"Nuciferous",{24,2}},"Polyhedron"]

Bilateral

GraphData[{"Nuciferous",{24,2}},"Graph","Bilateral"]//StyleGraphs

Circular

GraphData[{"Nuciferous",{24,2}},"Graph","Circular"]//StyleGraphs

Planar

GraphData[{"Nuciferous",{24,2}},"Planar"]

GraphData[{"Nuciferous",{24,2}},"Graph","Planar"]//StyleGraphs

MinimalCrossing

GraphData[{"Nuciferous",{24,2}},{"RCN","CN"}]

GraphData[{"Nuciferous",{24,2}},"Graph","MinimalCrossing"]//StyleGraphs

MinimalCrossing construction

(cn=CrossingNumber[GraphData[{"Nuciferous",{24,2}}],TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData[{"Nuciferous",{24,2}}],TimeConstraint->10])//AbsoluteTiming

(g=MinimalCrossingGraph[GraphData[{"Nuciferous",{24,2}}],"CrossingNumber"->cn])//PolyhedralGraphQ

faces=ReverseSort@SymmetricallyDistinctFaces[g]

Tally[ReverseSort[Length/@faces]]

IGLayoutTutte[g,"OuterFace"->#]&/@faces

Union[Select[Table[RotateGraph[MinimalCrossingGraph[GraphData[{"Nuciferous",{24,2}}],"CrossingNumber"->cn,RandomSeed->n]],{n,50}],Max[OuterFace[#]]<=GraphData[{"Nuciferous",{24,2}},"V"]&]]//Timing

Table[MinimalCrossingGraph[GraphData[{"Nuciferous",{24,2}}],"CrossingNumber"->cn,RandomSeed->i],{i,50}]//Union

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

RectilinearCrossingCount[g]

Circulant

GraphData[{"Nuciferous",{24,2}},"Circulant"]

GraphData[{"Nuciferous",{24,2}},"Graph","Circulant"]//StyleGraphs

Complement graph

GraphData[{"Nuciferous",{24,2}},"ComplementGraph","Name"]

Line graph

GraphData[{"Nuciferous",{24,2}},"Line"]

LineGraphQ[GraphData[{"Nuciferous",{24,2}}]]//Timing

RootGraph

Select[GraphData[All],GraphData[#,"LineGraph","Name"]=== {"Nuciferous",{24,2}}&]

RootGraph[GraphData[{"Nuciferous",{24,2}}]]

Halin

GraphData[{"Nuciferous",{24,2}},"Halin"]

GraphData[{"Nuciferous",{24,2}},"Graph","Halin"]//StyleGraphs

Rigid

GraphData[{"Nuciferous",{24,2}},"Rigid"]

GraphData[{"Nuciferous",{24,2}},"Graph","Rigid"]//StyleGraphs

Flexible

GraphData[{"Nuciferous",{24,2}},"Flexible"]

GraphData[{"Nuciferous",{24,2}},"Graph","Flexible"]//StyleGraphs

LCF

GraphData[{"Nuciferous",{24,2}},"LCF"]

GraphData[{"Nuciferous",{24,2}},"HamiltonianCycleCount"]

GraphData[{"Nuciferous",{24,2}},"LCFSignature"]

GraphData[{"Nuciferous",{24,2}},"LCFNotations"]

GraphData[{"Nuciferous",{24,2}},"Graph","LCF"]//StyleGraphs

Tally[LCFNotation[#][[2]]&/@%]

LCF compute random

FindRandomLCFNotation[GraphData[{"Nuciferous",{24,2}}],TimeConstraint->120]

LCF compute 10^5

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,2}}],10^5])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs]

LCF compute 10^6

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,2}}],10^6])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs]

LCF compute 10^7

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,2}}],10^7])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1|2}]

LCFGraph@@@DeleteCases[lcf,{_,1|2}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,3])]//Timing

Length[gs]

gs

LCF compute 5*^7

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,2}}],5*^7])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

DeleteCases[lcf,{_,1|2}]

LCFGraph@@@DeleteCases[lcf,{_,1|2}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,3])]//Timing

Length[gs]

gs

nicelcf=Cases[LCFNotation/@gs,{_,6}]

l={{{"Nuciferous",{24,2}},{0,Missing["NotAvailable",{{{{-12,-11,-6,-4,4},{-12,-10,-8,8,11},{-12,-3,5,6,9},{-12,-9,-5,3,10}},6}}]}}}

PropertyReplace[l,"LCFNotations","14.1"]

RenameGraphFiles[]

LCF compute all

Length[FindHamiltonianCycle[GraphData[{"Nuciferous",{24,2}}],All][[All,All,1]]]//Timing

Tally[(lcf=LCF[GraphData[{"Nuciferous",{24,2}}],All])[[All,2]]]//Timing

MaxMemoryUsed[]/10.^9 "GB"

Tally[(lcf=ReadProperty["LCFNotations",GraphNameToFileName[{"Nuciferous",{24,2}},".m.gz"]])[[All,2]]]//Timing

DeleteCases[lcf,{_,1}]

LCFGraph@@@DeleteCases[lcf,{_,1}]//StyleGraphs

Tally[LCFNotation[#][[-1]]&/@(gs=NiceLCFGraphs[lcf,2,1])]//Timing

Length[gs]

gs

UnitDistance

GraphData[{"Nuciferous",{24,2}},"UnitDistance"]

UnitDistanceGraphQ[GraphData[{"Nuciferous",{24,2}}],Debug->True]//Timing

GraphData[{"Nuciferous",{24,2}},"Graph","UnitDistance"]//StyleGraphs

UnitDistance by refinement

UnitDistanceEmbeddingRefine[Graph[GraphData[{"Nuciferous",{24,2}},"VertexList"],GraphData[{"Nuciferous",{24,2}},"EdgeList"]],MaxIterations->500]

UnitDistanceEmbeddingRefine[Annotate[#,VertexCoordinates->N[GraphEmbedding[#]]],MaxIterations->500]&/@Complement@@(GraphData[{"Nuciferous",{24,2}},"Graph",#]&/@{"All","UnitDistance"})

UnitDistance by FindUnitDistanceEmbedding

FindUnitDistanceEmbedding[GraphData[{"Nuciferous",{24,2}}],MaxIterations->5000,"ReturnWithMessage"->True]//Timing

FindUnitDistanceEmbedding[GraphData[{"Nuciferous",{24,2}}],MaxIterations->5000,"ReturnWithMessage"->False]//Quiet//Timing

UnitDistance by FindSubgraphUnitDistanceEmbedding

{{"Nuciferous",{24,2}},l=FindSubgraphUnitDistanceEmbedding[GraphData[{"Nuciferous",{24,2}}],TimeConstraint->300,"Results"->All]//Timing}

gs=SortBy[UniqueEmbeddings[l],Replace[RectilinearCrossingCount[#],Infinity->0]&]

Matchstick

GraphData[{"Nuciferous",{24,2}},"Matchstick"]

GraphData[{"Nuciferous",{24,2}},"Graph","Matchstick"]//StyleGraphs

3D default

Graph3D[GraphData[{"Nuciferous",{24,2}},"Edges"]]

3D All

GraphData[{"Nuciferous",{24,2}},"Graph",{"3D","All"}]

3D UnitDistance

GraphData[{"Nuciferous",{24,2}},"Graph",{"3D","UnitDistance"}]

3D Polyhedron

GraphData[{"Nuciferous",{24,2}},"Polyhedral"]

GraphData[{"Nuciferous",{24,2}},"Graph",{"3D","Polyhedron"}]

Examples

(Subscript[P, 2])

(adj=AdjacencyMatrix[PathGraph[{1,2}]])//MatrixForm//TraditionalForm

Det[adj]

Inverse[adj]//MatrixForm//TraditionalForm

NuciferousGraphQ[PathGraph[{1,2}]]

GraphData

GraphDataString

Length[gs=Join[
{24,#}&/@{1172,1179,13325,13994,13996,14035},
{28,#}&/@{10287,16362,17704},
{30,#}&/@{8077,23514,23612,23902,24388,24393,25409,25824,26697,27267,27814,45788}
]]

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Royle/VertexTransitive/"];

Length[vt[#]=Import["trans"<>ToString[#]<>".g6"]]&/@{24 ,28,30}//AbsoluteTiming

GraphData[{"VertexTransitive",{12,28}},"StandardNames"]

GraphData[{"VertexTransitive",{12,28}},"Names"]

Options[GraphDataString]

Re-run

24

Close[file]

28, 30

file=OpenAppend["~/nuciferous.m"]

(cnt[#]=0)&/@{24,28,30};
WriteString[file,GraphDataString[vt[#1][[#2]],
"StandardName"->{"Nuciferous",{#1,++cnt[#1]}},
"AlternateStandardNames"->{{"VertexTransitive",{#1,#2}}},
"Name"->ToString[#1]<>"\[Hyphen]nuciferous graph "<>ToString[cnt[#1]],
"AlternateNames"->{ToString[#1]<>"\[Hyphen]vertex transitive graph "<>ToString[#2]},
"Classes"->{"Cayley","Nuciferous"},
"Information"->"NuciferousGraph",
"Skip"->{"ChromaticPolynomial"},
TimeConstraint->60,
Debug->True
]]&@@@DeleteCases[gs,{24,_}];

Close[file]