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:
“The mountain stood there to be pointed at.
Pasture ran up the side a little way,
And then there was a wall of trees with trunks;
After that only tops of trees, and cliffs
Imperfectly concealed among the leaves.”
—Robert Frost (1874–1963)
“Let us have a good many maples and hickories and scarlet oaks, then, I say. Blaze away! Shall that dirty roll of bunting in the gun-house be all the colors a village can display? A village is not complete, unless it have these trees to mark the season in it. They are important, like the town clock. A village that has them not will not be found to work well. It has a screw loose, an essential part is wanting.”
—Henry David Thoreau (1817–1862)
“It was when the trees were leafless first in November
And their blackness became apparent, that one first
Knew the eccentric to be the base of design.”
—Wallace Stevens (1879–1955)