Asymetric graph with three nods

Thread starter Tom83B
Start date Dec 30, 2012
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Graph

AI Thread Summary

The discussion centers on the asymmetry of a specific graph configuration with three nodes. It questions why the graph is not considered asymmetric, noting that there appears to be only one automorphism present. The conclusion reached is that the graph cannot be asymmetric due to the existence of non-trivial symmetries, specifically the permutation (1 2). This realization clarifies the initial confusion regarding the graph's properties. The conversation highlights the importance of understanding graph symmetries in determining asymmetry.

Dec 30, 2012

Tom83B

Why isn't this graph:
1-2 3
asymetric?
I think there exists only one automorphism:
2-1 3
but I'm also supposed to prove that ther are no asymetric graphs with 1<|V(G)|<=5
so it can't be assymetric

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Dec 30, 2012

Tom83B

Oh I see now! It can have no non-trivial symmetries and permutation (1 2) is already a non-trivial symmetry.
Sorry to bother

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