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By torus grid I mean a graph with $n \times m$ vertices $v_{ij}$ and edges $\{(v_{i,j}, v_{(i+1) \mod n,j})\} \cup \{(v_{ij},v_{i,(j+1) \mod m})\}$.

By automorphism here I mean a permutation $\pi$ over the set of the graph's edges such that there is a permutation $\psi$ over the set of the vertices such that $\pi(u,v) = (\psi(u), \psi(v))$

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  • $\begingroup$ Do you know the orbit-stabilizer theorem? It seems like it would work pretty well here. $\endgroup$
    – pjs36
    Mar 8, 2017 at 0:49
  • $\begingroup$ It helps to calculate the number of automorphisms, isn't it? $\endgroup$ Mar 8, 2017 at 8:02

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