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Problem 6 (Automorphisms Of A Square)
Consider the graph $\mathcal{G} = (V,E)$ drawn below. The vertex set is $V = \{1,2,3,4\}$ and the set of edges is $$E = \{\{1,2\},\{2,3\},\{3,4\},\{1,4\}\}.$$
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 AutomorphismsOfASquare2.
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