Create a Figure with a sequence of Balanced Binary Trees

Question

I would like make the attached image by Mathematica. someone who could help me? Thank! enter image description here

And at least but not last.., have you even tried anything? Like getting the coordinates of the points? — Öskå, Jun 12 '14 at 15:05
Now I just saw the comments ... thanks everyone for the help — user15850, Jun 13 '14 at 06:46

score 6 · Answer 1 · answered Jun 12 '14 at 16:09

Not a perfect match but a start

Partition[Table[Column[{"i = " <> ToString[2^(n - 1)], 
 CompleteKaryTree[n, 
  ImagePadding -> 
   10, (AbsoluteOptions[
     CompleteKaryTree[n, VertexLabels -> "Name", ImagePadding -> 10], 
     VertexCoordinates] /. {x_?NumericQ, y_?NumericQ} :> {x, -y})], 
 "\[Omega] = " <> ToString[n]}, Center], {n, 2, 5}], 2] // Grid

enter image description here

kglr · Answer 2 · 2014-06-13T09:32:40.040

6

If you have Version 9, you can use the GraphLayout suboptions as follows:

bbt[n_] := 
Labeled[GraphUnion[CompleteKaryTree[n], Graph[{UndirectedEdge[0, 1]}],
                   BaseStyle ->Directive[Opacity[1], Black, PointSize[.015]],
                   EdgeStyle -> Directive[{Black, Thick}], AspectRatio -> 1,
                   VertexShapeFunction -> "Point",  ImageSize -> 300,
                   GraphLayout -> {"LayeredEmbedding", "RootVertex" -> 0,
                                   "Orientation" -> Bottom, 
                                   LayerSizeFunction -> (If[# == 1, 1, 2^(n - #)] &)}],
       {"i = " <> ToString[2^(n - 1)],"\[Omega] = " <> ToString[n]}, 
       {Top, Bottom}];

Row[bbt /@ Range[2,7], Spacer[5]]

enter image description here

edited Jun 13 '14 at 09:32

answered Jun 13 '14 at 03:01

kglr

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I'm afraid that it doesn't look the same on v8. None of the GraphLayout options seem to work for me. – Öskå Jun 13 '14 at 09:26
@Öskå, right - these GraphLayout options are new-in-version-9. – kglr Jun 13 '14 at 09:31
Well, they seem to be very useful! You already have my +1 – Öskå Jun 13 '14 at 09:38
@Oska, thank you for the +. – kglr Jun 13 '14 at 09:50
Well, your output looks like what the OP desired, the raw one from CompleteKaryTree is getting flatter and flatter. – Öskå Jun 13 '14 at 09:52

Create a Figure with a sequence of Balanced Binary Trees

2 Answers2