Wolfram Cloud Document

<<"NetworkSystems/NewGraphs.m"

Install["NetworkSystems/NewGraphsLink"]

LinkObject[NetworkSystems/NewGraphsLink, 57, 6]

rlist={bkr[1,1],bkr[1,2],bkr[2,1],bkr[2,2],bkr[2,3],bkr[3,1],bkr[3,2],bkr[3,3],bkr[3,4]};

(Length/@XGCEvolveList[{#1},tetragraph,5]&)/@rlist

{{6, 6, 6, 6, 6, 6}, {6, 12, 12, 12, 12, 12},

{6, 6, 6, 6, 6, 6}, {6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6}, {6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6}, {6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6}}

Length/@XGCEvolveList[{bkr[1,2],bkr[1,1]},tetragraph,5]

{6, 12, 12, 12, 12, 12}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,3]},tetragraph,8]

{6, 12, 9, 27, 45, 99, 189, 387, 765}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,1]},tetragraph,8]

{6, 12, 12, 30, 42, 96, 168, 354, 678}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,2]},tetragraph,8]

{6, 12, 12, 30, 42, 96, 168, 354, 678}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,1],bkr[3,3]},tetragraph,8]

{6, 12, 12, 30, 42, 96, 168, 354, 678}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,4]},tetragraph,8]

{6, 12, 15, 33, 63, 129, 255, 513, 1023}

Length/@XGCEvolveList[{bkr[1,1],bkr[3,1]},tetragraph,8]

{6, 6, 6, 6, 6, 6, 6, 6, 6}

Length/@XGCEvolveList[{bkr[1,1],bkr[3,4]},tetragraph,8]

{6, 6, 9, 9, 9, 9, 9, 9, 9}

combs=DeleteCases[DeleteCases[Flatten[Outer[List,{Null,b[1,1],b[1,2]},{Null,b[2,1],b[2,2],b[2,3]},{Null,b[3,1],b[3,2],b[3,3],b[3,4]}],2],Null,{2}],{}]

{{b[3, 1]}, {b[3, 2]}, {b[3, 3]}, {b[3, 4]}, {b[2, 1]},

{b[2, 1], b[3, 1]}, {b[2, 1], b[3, 2]},

{b[2, 1], b[3, 3]}, {b[2, 1], b[3, 4]}, {b[2, 2]},

{b[2, 2], b[3, 1]}, {b[2, 2], b[3, 2]},

{b[2, 2], b[3, 3]}, {b[2, 2], b[3, 4]}, {b[2, 3]},

{b[2, 3], b[3, 1]}, {b[2, 3], b[3, 2]},

{b[2, 3], b[3, 3]}, {b[2, 3], b[3, 4]}, {b[1, 1]},

{b[1, 1], b[3, 1]}, {b[1, 1], b[3, 2]},

{b[1, 1], b[3, 3]}, {b[1, 1], b[3, 4]},

{b[1, 1], b[2, 1]}, {b[1, 1], b[2, 1], b[3, 1]},

{b[1, 1], b[2, 1], b[3, 2]},

{b[1, 1], b[2, 1], b[3, 3]},

{b[1, 1], b[2, 1], b[3, 4]}, {b[1, 1], b[2, 2]},

{b[1, 1], b[2, 2], b[3, 1]},

{b[1, 1], b[2, 2], b[3, 2]},

{b[1, 1], b[2, 2], b[3, 3]},

{b[1, 1], b[2, 2], b[3, 4]}, {b[1, 1], b[2, 3]},

{b[1, 1], b[2, 3], b[3, 1]},

{b[1, 1], b[2, 3], b[3, 2]},

{b[1, 1], b[2, 3], b[3, 3]},

{b[1, 1], b[2, 3], b[3, 4]}, {b[1, 2]},

{b[1, 2], b[3, 1]}, {b[1, 2], b[3, 2]},

{b[1, 2], b[3, 3]}, {b[1, 2], b[3, 4]},

{b[1, 2], b[2, 1]}, {b[1, 2], b[2, 1], b[3, 1]},

{b[1, 2], b[2, 1], b[3, 2]},

{b[1, 2], b[2, 1], b[3, 3]},

{b[1, 2], b[2, 1], b[3, 4]}, {b[1, 2], b[2, 2]},

{b[1, 2], b[2, 2], b[3, 1]},

{b[1, 2], b[2, 2], b[3, 2]},

{b[1, 2], b[2, 2], b[3, 3]},

{b[1, 2], b[2, 2], b[3, 4]}, {b[1, 2], b[2, 3]},

{b[1, 2], b[2, 3], b[3, 1]},

{b[1, 2], b[2, 3], b[3, 2]},

{b[1, 2], b[2, 3], b[3, 3]},

{b[1, 2], b[2, 3], b[3, 4]}}

rcombs=combs/.bbkr;

(Length/@XGCEvolveList[#1,tetragraph,8]&)/@rcombs

{{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023}}

Union[%]

{{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 15, 33, 63, 129, 255, 513, 1023}}

ratios[list_]:=N

Rest[list]

Drop[list,-1]



ratios/@%444

{{1., 0.5, 1., 1., 1., 1., 1., 1.},

{1., 1., 1., 1., 1., 1., 1., 1.},

{1., 1.5, 1., 1., 1., 1., 1., 1.},

{2., 0.75, 3., 1.66667, 2.2, 1.90909, 2.04762,

1.97674}, {2., 1., 1., 1., 1., 1., 1., 1.},

{2., 1., 2.5, 1.4, 2.28571, 1.75, 2.10714, 1.91525},

{2., 1.25, 2.2, 1.90909, 2.04762, 1.97674, 2.01176,

1.99415}}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,1]},tetragraph,10]

{6, 12, 12, 30, 42, 96, 168, 354, 678, 1380, 2724}

ratios[%]

{2., 1., 2.5, 1.4, 2.28571, 1.75, 2.10714, 1.91525,

2.0354, 1.97391}

ListPlot[%,PlotJoinedTrue];

%449-2RotateRight[%449]

{-5442, 0, -12, 6, -18, 12, -24, 18, -30, 24, -36}

Length/@XGCEvolveList[{bkr[1,2],bkr[3,1]},tetragraph,12]

{6, 12, 12, 30, 42, 96, 168, 354, 678, 1380, 2724, 5478,

10914}

%-2RotateRight[%]

{-21822, 0, -12, 6, -18, 12, -24, 18, -30, 24, -36, 30,

-42}

ListPlot[Rest[%],PlotJoinedTrue];

(Length/@XGCEvolveList[#1,{{1,2},{1,2},{1,2}},8]&)/@rcombs

{{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023},

{3, 9, 15, 33, 63, 129, 255, 513, 1023}}

Union[%]

{{3, 3, 3, 3, 3, 3, 3, 3, 3},

{3, 9, 15, 33, 63, 129, 255, 513, 1023}}

Table[MapThread[RotateRight,{{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}},IntegerDigits[i,2,6]}],{i,0,

-1}];

CanonicalGraph/@%;

Union[%]

{{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}},

{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {3, 4}, {4, 2}},

{{1, 2}, {1, 3}, {2, 3}, {2, 4}, {3, 4}, {4, 1}},

{{1, 2}, {1, 3}, {2, 3}, {2, 4}, {4, 1}, {4, 3}}}

alltetragraphs=%;

Function[g,(Length/@XGCEvolveList[#1,g,8]&)/@rcombs]/@alltetragraphs

{{{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606},

{6, 12, 18, 30, 54, 90, 162, 318, 606}},

{{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 3, 9, 15, 33, 63, 129, 255, 513},

{6, 9, 15, 33, 63, 129, 255, 513, 1023},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 3, 9, 15, 33, 63, 129, 255, 513},

{6, 9, 15, 33, 63, 129, 255, 513, 1023},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 3, 9, 15, 33, 63, 129, 255, 513},

{6, 9, 15, 33, 63, 129, 255, 513, 1023},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 3, 9, 15, 33, 63, 129, 255, 513},

{6, 9, 15, 33, 63, 129, 255, 513, 1023}},

{{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 9, 9, 9, 9, 9, 9, 9, 9}},

{{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 15, 33, 63, 129, 255, 513, 1023}}}

Union[Flatten[%,1]]

{{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 3, 9, 15, 33, 63, 129, 255, 513},

{6, 6, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 12, 12, 30, 42, 96, 168, 354},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 9, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 9, 27, 45, 99, 189, 387, 765},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 30, 42, 96, 168, 354, 678},

{6, 12, 15, 33, 63, 129, 255, 513, 1023},

{6, 12, 18, 30, 54, 90, 162, 318, 606}}

(Rest[#1-2RotateRight[#1]]&)/@%

{{-9, -3, -3, -3, -3, -3, -3, -3},

{-9, 3, -3, 3, -3, 3, -3, 3},

{-6, -9, -3, -3, -3, -3, -3, -3},

{-6, -6, -6, -6, -6, -6, -6, -6},

{-6, -3, -9, -9, -9, -9, -9, -9},

{-6, 0, -12, 6, -18, 12, -24, 18},

{-3, -9, -9, -9, -9, -9, -9, -9},

{-3, -3, 3, -3, 3, -3, 3, -3},

{0, -15, 9, -9, 9, -9, 9, -9},

{0, -12, -12, -12, -12, -12, -12, -12},

{0, -12, 6, -18, 12, -24, 18, -30},

{0, -9, 3, -3, 3, -3, 3, -3},

{0, -6, -6, -6, -18, -18, -6, -30}}

Length/@XGCEvolveList[{bkr[1,2]},alltetragraphs〚1〛,8]

{6, 12, 18, 30, 54, 90, 162, 318, 606}

Length/@XGCEvolveList[{bkr[1,2]},alltetragraphs〚1〛,12]

{6, 12, 18, 30, 54, 90, 162, 318, 606, 1218, 2394, 4806,

9558}

(Rest[#1-2RotateRight[#1]]&)[%]

{0, -6, -6, -6, -18, -18, -6, -30, 6, -42, 18, -54}

ListPlot[%,PlotJoinedTrue];

LINEAR GROWTH:

ladderer={{1,1},{1,2},{3,3},{3,2},{2,4},{5,4},{5,5},{6,4},{6,6}}

{{1, 1}, {1, 2}, {3, 3}, {3, 2}, {2, 4}, {5, 4}, {5, 5},

{6, 4}, {6, 6}}

Length/@XGCEvolveList[{bkr[1,2]},ladderer,20]

{9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87,

93, 99, 105, 111, 117, 123, 129}

ListPlot[%,PlotJoinedTrue];

Table[MapThread[RotateRight,{{{1,2},{1,2},{3,4},{3,4},{2,3},{4,1}},IntegerDigits[i,2,6]}],{i,0,

-1}];

CanonicalGraph/@%;

Union[%]

{{{1, 2}, {1, 2}, {1, 3}, {2, 4}, {3, 4}, {3, 4}},

{{1, 2}, {1, 2}, {1, 3}, {2, 4}, {3, 4}, {4, 3}},

{{1, 2}, {1, 2}, {1, 3}, {2, 4}, {4, 3}, {4, 3}},

{{1, 2}, {1, 2}, {1, 3}, {3, 4}, {3, 4}, {4, 2}},

{{1, 2}, {1, 2}, {1, 3}, {3, 4}, {4, 2}, {4, 3}},

{{1, 2}, {1, 2}, {1, 3}, {4, 2}, {4, 3}, {4, 3}},

{{1, 2}, {1, 2}, {2, 3}, {3, 4}, {3, 4}, {4, 1}},

{{1, 2}, {1, 2}, {2, 3}, {3, 4}, {4, 1}, {4, 3}},

{{1, 2}, {1, 2}, {3, 1}, {3, 4}, {4, 2}, {4, 3}},

{{1, 2}, {1, 3}, {2, 1}, {2, 4}, {3, 4}, {4, 3}},

{{1, 2}, {1, 3}, {2, 1}, {3, 4}, {4, 2}, {4, 3}}}

{{6, 3, 3, 3, 3, 3, 3, 3, 3},

{6, 6, 6, 6, 6, 6, 6, 6, 6},

{6, 6, 6, 9, 9, 9, 9, 9, 9},

{6, 6, 9, 9, 9, 9, 9, 9, 9},

{6, 6, 12, 18, 30, 54, 90, 186, 342},

{6, 9, 9, 9, 9, 9, 9, 9, 9},

{6, 9, 12, 12, 12, 12, 12, 12, 12},

{6, 9, 12, 24, 42, 78, 138, 246, 474},

{6, 9, 15, 21, 33, 45, 57, 69, 81},

{6, 9, 15, 27, 51, 93, 183, 345, 675},

{6, 12, 12, 12, 12, 12, 12, 12, 12},

{6, 12, 12, 24, 36, 72, 132, 264, 516},

{6, 12, 15, 27, 39, 63, 111, 183, 327},

{6, 12, 15, 27, 51, 93, 183, 345, 675},

{6, 12, 18, 30, 42, 54, 66, 78, 90},

{6, 12, 18, 30, 54, 90, 186, 342, 702},

{6, 12, 18, 30, 54, 102, 198, 390, 774},

{6, 12, 18, 33, 57, 93, 177, 309, 585},

{6, 12, 18, 33, 57, 105, 207, 393, 783},

{6, 12, 18, 36, 60, 108, 204, 396, 780},

{6, 12, 24, 48, 96, 192, 384, 768, 1536},

{6, 18, 30, 66, 126, 258, 510, 1026, 2046}}

{{-9, -3, -3, -3, -3, -3, -3, -3},

{-6, -6, -6, -6, -6, -6, -6, -6},

{-6, -6, -3, -9, -9, -9, -9, -9},

{-6, -3, -9, -9, -9, -9, -9, -9},

{-6, 0, -6, -6, -6, -18, 6, -30},

{-3, -9, -9, -9, -9, -9, -9, -9},

{-3, -6, -12, -12, -12, -12, -12, -12},

{-3, -6, 0, -6, -6, -18, -30, -18},

{-3, -3, -9, -9, -21, -33, -45, -57},

{-3, -3, -3, -3, -9, -3, -21, -15},

{0, -12, -12, -12, -12, -12, -12, -12},

{0, -12, 0, -12, 0, -12, 0, -12},

{0, -9, -3, -15, -15, -15, -39, -39},

{0, -9, -3, -3, -9, -3, -21, -15},

{0, -6, -6, -18, -30, -42, -54, -66},

{0, -6, -6, -6, -18, 6, -30, 18},

{0, -6, -6, -6, -6, -6, -6, -6},

{0, -6, -3, -9, -21, -9, -45, -33},

{0, -6, -3, -9, -9, -3, -21, -3},

{0, -6, 0, -12, -12, -12, -12, -12},

{0, 0, 0, 0, 0, 0, 0, 0}, {6, -6, 6, -6, 6, -6, 6, -6}}

{{10, 55}, {10, 56}, {10, 57}, {10, 58}, {10, 59}}

{{2, 55}, {2, 56}, {2, 57}, {2, 58}, {2, 59}}

{{5, 50}, {5, 51}, {5, 52}, {5, 53}, {5, 54}}

{{9, 50}, {9, 51}, {9, 52}, {9, 53}, {9, 54}}

{{9, 55}, {9, 56}, {9, 57}, {9, 58}, {9, 59}}

{{b[1, 2], b[2, 2]}, {b[1, 2], b[2, 2], b[3, 1]},

{b[1, 2], b[2, 2], b[3, 2]},

{b[1, 2], b[2, 2], b[3, 3]},

{b[1, 2], b[2, 2], b[3, 4]}, {b[1, 2], b[2, 3]},

{b[1, 2], b[2, 3], b[3, 1]},

{b[1, 2], b[2, 3], b[3, 2]},

{b[1, 2], b[2, 3], b[3, 3]},

{b[1, 2], b[2, 3], b[3, 4]}}

{b[1, 2], b[2, 2]}

{b[1, 2], b[2, 3]}

LinkObject::linkd:
LinkObject[NetworkSystems/NewGraphsLink, <<2>>]
is closed; the connection is dead.

{6, 12, 15, 27, 39, 63, 111, 183, 327, 591, 1119, 2151,

4215, 8319, 0}

{0, -9, -3, -15, -15, -15, -39, -39, -63, -63, -87, -87,

-111}

{6, 12, 18, 33, 57, 93, 177, 309, 585, 1101, 2145, 4197,

8313}

{0, -6, -3, -9, -21, -9, -45, -33, -69, -57, -93, -81}

{6, 9, 12, 24, 42, 78, 138, 246, 474, 918, 1818, 3606,

7194}

{-3, -6, 0, -6, -6, -18, -30, -18, -30, -18, -30, -18}

{6, 9, 15, 27, 51, 93, 183, 345, 675, 1341, 2655, 5313,

10587}

{-3, -3, -3, -3, -9, -3, -21, -15, -9, -27, 3, -39}

{6, 9, 15, 27, 51, 93, 183, 345, 675, 1341, 2655, 5313,

10587, 21189, 42327}

{-3, -3, -3, -3, -9, -3, -21, -15, -9, -27, 3, -39, 15,

-51}

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

1, 1, 1, 1, 1, 1, 1, 1, 1}

{{2}, {1}, {1, 1}, {1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

1, 1, 1, 1, 1, 1, 1, 1, 1}}

{6, 12, 18, 33, 57, 105, 207, 393, 783, 1521, 3063,

6057, 12159}

{0, -6, -3, -9, -9, -3, -21, -3, -45, 21, -69, 45}

$Aborted

Union::normal:
Normal expression expected at position 1 in
Union[$Aborted].

Union[$Aborted]