Find the number of all possible automorphisms for the following graph
So, this question was in my exam yesterday and I wrote $36$ as an answer. I just want to know if my answer is correct. Thanks for the help in advance
2026-05-17 15:35:05.1779032105
Find the number of all possible automorphisms for the given graph
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Consider the above coloring of your graph. The blue edges are part of a triangle, and the red edges are not. So any automorphism of the graph must map red edges to red edges and blue edges to blue edges. Any automorphism of the graph must therefore also be an automorphism of the red cycle.
Now there are $18$ automorphisms of the red cycle (identity, rotations and reflections) and each of them is also an automorphism of the given graph. So the total number of automorphisms of the given graph is also $18$.