Trees
The smallest asymmetric tree has seven vertices: it consists of three paths of lengths 1, 2, and 3, linked at a common endpoint. In contrast to the situation for graphs, almost all trees are symmetric. In particular, if a tree is chosen uniformly at random among all trees on n labeled nodes, then with probability tending to 1 as n increases, the tree will contain some two leaves adjacent to the same node and will have symmetries exchanging these two leaves.
Read more about this topic: Asymmetric Graph
Famous quotes containing the word trees:
“For beauty, give me trees with the fur on.”
—Henry David Thoreau (1817–1862)
“Though trees turn bare and girls turn wives,
We shall afford our costly seasons;
There is a gentleness survives
That will outspeak and has its reasons.
There is a loveliness exists,
Preserves us, not for specialists.”
—William Dewitt Snodgrass (b. 1926)
“Below me trees unnumbered rise,
Beautiful in various dyes:
The gloomy pine, the poplar blue,
The yellow beech, the sable yew,
The slender fir that taper grows,
The sturdy oak with broad-spread boughs.”
—John Dyer (1699–1758)