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 trees persist, yeasty and sensuous,
as thick as saints.”
—Anne Sexton (1928–1974)
“The very dew seemed to hang upon the trees later into the day than usual, as on the sides of mountains.”
—Henry David Thoreau (1817–1862)
“At twelve, the disintegration of afternoon
Began, the return to phantomerei, if not
To phantoms. Till then, it had been the other way:
One imagined the violet trees but the trees stood green,
At twelve, as green as ever they would be.
The sky was blue beyond the vaultiest phrase.”
—Wallace Stevens (1879–1955)