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How to make colors of edges in CayleyGraph ?

Yoshihiro Sato

Posted 11 years ago

My question is how to make colors of edges in CayleyGraph. This is an example. group = PermutationGroup[pp] PermutationGroup[{Cycles[{{5, 8, 6}}], Cycles[{{4, 7, 8, 6, 5}}], Cycles[{{2, 5, 8, 6, 3}}], Cycles[{{1, 4, 7, 8, 6, 5, 2}}], Cycles[{{1, 4, 7, 8, 6, 3, 2}}], Cycles[{{2, 5, 4, 7, 8, 6, 3}}], Cycles[{{1, 4, 5, 8, 6, 3, 2}}]}] cayleygraph = CayleyGraph[group]; There are seven colors of edges in CayleyGraph. My trial to make colors is as follows. colors = Hue[#] & /@ ((1/7)*{0, 1, 2, 3, 4, 5, 6} // N) {Hue[0.], Hue[0.14285714285714285`], Hue[0.2857142857142857], Hue[0.42857142857142855`], Hue[0.5714285714285714], Hue[0.7142857142857143], Hue[0.8571428571428571]} I want to know whether it is correct or not for edge colors of CayleyGraph. Thanks, Yoshihiro Sato

My question is how to make colors of edges in CayleyGraph. This is an example.

group = PermutationGroup[pp]
     PermutationGroup[{Cycles[{{5, 8, 6}}], Cycles[{{4, 7, 8, 6, 5}}], 
      Cycles[{{2, 5, 8, 6, 3}}], Cycles[{{1, 4, 7, 8, 6, 5, 2}}], 
      Cycles[{{1, 4, 7, 8, 6, 3, 2}}], Cycles[{{2, 5, 4, 7, 8, 6, 3}}], 
      Cycles[{{1, 4, 5, 8, 6, 3, 2}}]}]

cayleygraph = CayleyGraph[group];

There are seven colors of edges in CayleyGraph. My trial to make colors is as follows.

colors = Hue[#] & /@ ((1/7)*{0, 1, 2, 3, 4, 5, 6} // N)
   {Hue[0.], Hue[0.14285714285714285`], Hue[0.2857142857142857], 
    Hue[0.42857142857142855`], Hue[0.5714285714285714], Hue[0.7142857142857143], Hue[0.8571428571428571]}

I want to know whether it is correct or not for edge colors of CayleyGraph.

Thanks, Yoshihiro Sato

POSTED BY: Yoshihiro Sato

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Yoshihiro Sato

Posted 11 years ago

POSTED BY: Yoshihiro Sato

Simon Cadrin

Simon Cadrin, autodidacte

Posted 11 years ago

CayleyGraph[ PermutationGroup[{Cycles[{{5, 8, 6}}], Cycles[{{4, 7, 8}}]}], VertexLabels -> Placed["Name", Center], VertexSize -> 1.5]

POSTED BY: Simon Cadrin

Yoshihiro Sato

Posted 11 years ago

Hello Simon, Thank you for your suggestion. Documentation of CayleyGraph says that this is only a useful representation for small groups, and for groups with a few hundred elements is generally already too complex. I hope we can get a value of vertices and edges of CayleyGraph for large group if possible, although the graph is complicated. I have tried to use a CayleyGraph for small group, which is very interesting for me. Thanks, Yoshihiro Sato Attachments: