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)
“It is as when a migrating army of mice girdles a forest of pines. The chopper fells trees from the same motive that the mouse gnaws them,—to get his living. You tell me that he has a more interesting family than the mouse. That is as it happens.”
—Henry David Thoreau (1817–1862)
“I am a rose of Sharon, a lily of the valleys. As a lily among brambles, so is my love among maidens. As an apple tree among the trees of the wood, so is my beloved among young men. With great delight I sat in his shadow, and his fruit was sweet to my taste.”
—Bible: Hebrew, Song of Solomon 2:1-3.