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:
“They are very proper forest houses, the stems of the trees collected together and piled up around a man to keep out wind and rain,—made of living green logs, hanging with moss and lichen, and with the curls and fringes of the yellow birch bark, and dripping with resin, fresh and moist, and redolent of swampy odors, with that sort of vigor and perennialness even about them that toadstools suggest.”
—Henry David Thoreau (1817–1862)
“Bright yellow, red, and orange,
The leaves come down in hosts;
The trees are Indian princes,
But soon they’ll turn to ghosts;”
—William Allingham (1824–1889)
“The actor should not play a part. Like the Aeolian harps that used to be hung in the trees to be played only by the breeze, the actor should be an instrument played upon by the character he depicts.”
—Alla Nazimova (1879–1945)