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:
“an endless wind
Whips at the headstones of the dead and wails
In the trees for all who have and have not sinned.”
—Anthony Hecht (b. 1923)
“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)
“the broad cloud-driving moon in the clear sky
Lifts o’er the firs her shining shield,
And in her tranquil light
Sleep falls on forest and field.
See! sleep hath fallen: the trees are asleep:
The night is come. The land is wrapt in sleep.”
—Robert Bridges (1844–1930)