{{1,2},{2,1}}{{2,3},{3,2}
Permute elements in a relation; does the rule stay unchanged?
Permute elements in a relation; does the rule stay unchanged?
GraphAutomorphismGroup[
In[]:=
GraphAutomorphismGroup
Out[]=
PermutationGroup[{Cycles[{{3,6},{5,7},{8,10}}],Cycles[{{2,5,10,9,8,7},{3,6,4}}],Cycles[{{1,2},{3,7},{5,6}}]}]
In[]:=
GraphAutomorphismGroup[Graph[Rule@@@{{x,y},{y,z},{z,x}}]]
Out[]=
PermutationGroup[{Cycles[{{1,2,3}}]}]
Can one find rules that give particular automorphism groups?
Do LHS’es have symmetries ... and then do the rewrites preserve them?
Do LHS’es have symmetries ... and then do the rewrites preserve them?
E.g.
{{1,2},{2,1}}{{2,1},{3,2},{1,1}}
In[]:=
FindCanonicalWolframModel[{{x,y}}{{x,y},{y,z},{z,x}}]
Out[]=
{{1,2}}{{1,2},{2,3},{3,1}}
In[]:=
FindCanonicalWolframModel[{{y,x}}->{{y,x},{x,z},{z,y}}]
Out[]=
{{1,2}}{{1,2},{2,3},{3,1}}
In[]:=
FindCanonicalWolframModel[{{x,y}}->{{y,x},{x,z},{z,y}}]
Out[]=
{{1,2}}{{1,3},{2,1},{3,2}}
Do LHS and RHS separately have a certain invariance under renamings?
Symmetric graphs: https://www.wolframscience.com/nks/notes-9-8--symmetric-graphs/
In[]:=
GraphData["Symmetric"]
Out[]=
What is the analog of totalistic rules for graphs?
What is the analog of totalistic rules for graphs?
Perhaps there exist multiple rules, covering different cases that compute only the total number a given piece of graph structure [???]