Examples
The smallest asymmetric non-trivial graphs have 6 vertices. The smallest asymmetric regular graphs have ten vertices; there exist ten-vertex asymmetric graphs that are 4-regular and 5-regular. One of the two smallest asymmetric cubic graphs is the twelve-vertex Frucht graph discovered in 1939. According to a strengthened version of Frucht's theorem, there are infinitely many asymmetric cubic graphs.
Read more about this topic: Asymmetric Graph
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