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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Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (16881744)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (16701733)