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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“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
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—Bernard Mandeville (1670–1733)
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—G.C. (Georg Christoph)