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:
“A lake is the landscape’s most beautiful and expressive feature. It is earth’s eye; looking into which the beholder measures the depth of his own nature. The fluviatile trees next the shore are the slender eyelashes which fringe it, and the wooded hills and cliffs around are its overhanging brows.”
—Henry David Thoreau (1817–1862)