How can I determine orbits of dihedral group $D_n$? Any relevant references will be useful.
I consider cycle graph with $n$ vertices and (as I understand) its automorphism group is $D_n$. Then, consider adjacency matrix of this graph, $A$. I use the following definition of group orbit: $$\phi(G,i)=\lbrace\pi(i)\mid \pi\in G\rbrace,$$ where $G=\text{Aut}(A)$.
I have virtually zero knowledge in group theory, so my qeustion may be is not clear.