Consider the graph $\mathcal{G} = (V,E)$ drawn below. The vertex set is $V = \{1,2,3,4\}$ and the set of edges is $$E = \{\{1,2\},\{2,3\},\{3,4\},\{1,4\}\}.$$

%center%http://bmw.byuimath.com/aa/lib/exe/fetch.php?cache=&media=wiki:graphpictures:labeledsquare.png%%

Write down all the automorphisms of $\mathcal{G}$ (there are more than 4, but less than 10). Explain how you know you have listed every automorhpism of $\mathcal{G}$.

This problem continues in Problem/AutomorphismsOfASquare2.

• Make remarks with a list.

problem.automorphisms_of_a_square.tex

%%%%%
% DEPENDENCIES
% RequiredPackages: \usepackage{tikz}
% RequiredMacros: \DeclareMathOperator{\aut}{Aut} 
%%%%%
\begin{problem}
Consider the graph $\mathcal{G} = (V,E)$ drawn below. 
The vertex set is $V = \{1,2,3,4\}$ and the set of edges is $$E = \{\{1,2\},\{2,3\},\{3,4\},\{1,4\}\}.$$
 
%center%http://bmw.byuimath.com/aa/lib/exe/fetch.php?cache=&media=wiki:graphpictures:labeledsquare.png%%
 
Write down all the automorphisms of $\mathcal{G}$ (there are more than 4, but less than 10). Explain how you know you have listed every automorhpism of  $\mathcal{G}$. 
 
This problem continues in [[Problem/AutomorphismsOfASquare2]].
\end{problem}

• Dihedral group

problem ben