In[]:=
MultiwaySystem[{"AB""BA","BA""AB"},StringTuples["AB",6],10,"StatesGraph"]
Out[]=
In[]:=
Groupify[{gens:{__String},rels_}]:=Module[{igens=ToLowerCase[gens]},{Flatten@{gens,igens},Flatten[{rels,ToLowerCase[#2]ToLowerCase[#1]&@@@rels,Table[{gens[[i]]<>igens[[i]]"",igens[[i]]<>gens[[i]]""},{i,Length[gens]}]}]}]
Groupify
In[]:=
TreePlot[Graph[CayleyNestGraph[{{"A","B"},{"AAA"""}},{""},6],GraphLayout"SpringElectricalEmbedding"],Center]
Out[]=
In[]:=
TreePlot[Graph[CayleyNestGraph[{{"A","B"},{"AA"""}},{""},6],GraphLayout"SpringElectricalEmbedding"],Center,VertexLabelsAutomatic]
Out[]=
In[]:=
GraphElementData["EdgeShapeFunction"]
Out[]=
{Arrow,BoxLine,CarvedArcArrow,CarvedArrow,DashedLine,DiamondLine,DotLine,DottedLine,FilledArcArrow,FilledArrow,HalfFilledArrow,HalfFilledDoubleArrow,HalfUnfilledArrow,HalfUnfilledDoubleArrow,Line,ShortCarvedArcArrow,ShortCarvedArrow,ShortFilledArcArrow,ShortFilledArrow,ShortUnfilledArcArrow,ShortUnfilledArrow,UnfilledArcArrow,UnfilledArrow}
In[]:=
TreePlot[Graph[CayleyNestGraph[{{"A","B"},{"AA"""}},{""},4],GraphLayout"SpringElectricalEmbedding"],Center,VertexLabelsAutomatic,EdgeLabels(DirectedEdge[x_,y_]If[StringLength[y]0,"",StringTake[y,-1]])]
Out[]=
In[]:=
TreePlot[Graph[CayleyNestGraph[{{"A","B"},{"AB""BA","BA""AB"}},{""},6],GraphLayout"SpringElectricalEmbedding"],Center,VertexLabelsAutomatic]
Out[]=
Reduction of the tree by the relations is revealed in cycles, which are the edges in the states graph
Cayley graph is more about events than states....
Cayley graph is more about events than states....
Cayley graph edges just add generators on the right
Cayley graph edges just add generators on the right
Cayley graph colors:
Cayley graph colors:
Multiway graph from group
Multiway graph from group