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# How to make colors of edges in CayleyGraph ?

Posted 9 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
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Posted 9 years ago
 Hello,I could solve the problem using GroupElementToWord. I would like to report a 15 puzzle solver, which uses Graph and PermutationGroup. Please access my blog in Japanese.GridGraph[3,3]GridGraph[4,4]
Posted 9 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:
Posted 9 years ago
 CayleyGraph[ PermutationGroup[{Cycles[{{5, 8, 6}}], Cycles[{{4, 7, 8}}]}], VertexLabels -> Placed["Name", Center], VertexSize -> 1.5] 
Posted 9 years ago
 This group is the same as AlternatingGroup[8]. group = 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}}]}]; group == AlternatingGroup[8] True GroupOrder[group] 20160 cayleygraph = CayleyGraph[group]; {VertexCount[cayleygraph], EdgeCount[cayleygraph]} {20160, 141120} The document of CayleyGraph says that generators are represented default using different colors, with increasing Hue values for the elements listed GroupGenerators. But it does not say how the Hue are calculated.I have tries to use the following colors in CayleyGraph, but had no correct result. I wonder whether the color in CayleyGraph is correct. Anyone would tell me how to find out whether it is correct.Thanks, Yoshihiro SatoMy trial: ShortestPath in CayleyGraph 1 -> 10 Attachments:
Posted 9 years ago
 CayleyGraph[PermutationGroup[{Cycles[{{1, 5, 4}}], Cycles[{{3, 4}}]}], VertexLabels -> Placed["Name", Center], VertexSize -> 0.8]