In[]:=
Graph[MultiwaySystem[{"A""AB"},"AA",7,"EvolutionGraph"],GraphLayout"LayeredDigraphEmbedding",AspectRatio1/2,Epilog{Purple,Thick,Table[Line[{{-8,i},{8,i}}],{i,1/2,6+1/2}]}]
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Table[Graph[MultiwaySystem[{"A""AB"},"AA",t,"BranchialGraph"],ImageSize{600,30}],{t,1,7}]//Column
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ClearAll[straightFoliationLines];straightFoliationLines[{lineDensityHorizontal_:1,lineDensityVertical_:1},{tanHorizontal_:0.0,tanVertical_:0.0},transform_:(#&),offset_:{0,0},style_:Red]:={If[lineDensityHorizontal≠0,Style[Table[Line[transform/@{{-100+offset〚1〛,k-100tanHorizontal+offset〚2〛},{100+offset〚1〛,k+100tanHorizontal+offset〚2〛}}],{k,-100.5,100.5,1/lineDensityHorizontal}],style],{}],If[lineDensityVertical≠0,Style[Table[Line[transform/@{{k-100tanVertical+offset〚1〛,-100+offset〚2〛},{k+100tanVertical+offset〚1〛,100+offset〚2〛}}],{k,-100.5,100.5,1/lineDensityVertical}],style],{}]}
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Graph[MultiwaySystem[{"A""AB"},"AA",7,"EvolutionGraph"],GraphLayout"LayeredDigraphEmbedding",AspectRatio1/2,Epilog{Thick,straightFoliationLines[{1,0},{0.3,0},#&,{0,0},Purple]}]
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MultiwaySystem[{"A""AB"},"AA",2,"BranchialGraph"]
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Framed[Subgraph[MultiwaySystem[{"A""AB"},VertexList[MultiwaySystem[{"A""AB"},{"AA"},7,"StatesGraph"]],1,"BranchialGraph"],#,ImageSize{600,90}]]&/@{{"AA"},{"ABA","AAB","ABBA"},{"ABAB","AABB","ABBBA"},{"ABBAB","ABABB","ABBBBA","ABBBAB","ABBBBBA"},{"AABBB","ABBABB","ABBBBAB","ABBBBBBA","ABBBBBAB"},{"ABABBB","AABBBB","ABBBABB","ABBABBB","ABBBBABB","ABBBBBBBA","ABBBBBBAB"},{"ABABBBB","ABBBABBB","ABBBBBABB"},{"AABBBBB","ABBABBBB","ABABBBBB","ABBBBABBB","ABBBABBBB"},{"AABBBBBB","ABBABBBBB"},{"ABABBBBBB","AABBBBBBB"}}//Column
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