(botany) A perennial woody plant at least 20 feet (6 meters) in height at maturity, having an erect stem or trunk and a well-developed crown or leaf canopy.
(computer science) A data structure in which each element may be logically followed by two or more other elements, there is one element with no predecessor, every other element has a unique predecessor, and there are no circular lists.
(electronics) A set of connected circuit branches that includes no meshes; responds uniquely to each of the possible combinations of a number of simultaneous inputs. Also known as decoder.
(mathematics) A connected graph contained in a given connected graph having all the vertices of the original but without any closed circuit.
(metallurgy) A projecting treelike aggregate of crystals formed at areas of high local current density in electroplating.
Tree
| Sci-Tech Dictionary: tree |
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A perennial woody plant at least 20 ft (6 m) in height at maturity, having an erect stem or trunk and a well-defined crown or leaf canopy. However, no sharp lines can be drawn between trees, shrubs, and lianas (woody vines). The essence of the tree form is relatively large size, long life, and a slow approach to reproductive maturity. The difficulty of transporting water, nutrients, and storage products over long distances and high into the air against the force of gravity is a common problem of large treelike plants and one that is not shared by shrubs or herbs.
Classification
Almost all existing trees belong to the seed plants (Spermatophyta). An exception are the giant tree ferns which were more prominent in the forests of the Devonian Period and today exist only in the moist tropical regions. The Spermatophyta are divided into the Pinophyta (gymnosperms) and the flowering plants, Magnoliophyta (angiosperms). The gymnosperms bear their seed naked on modified leaves, called scales, which are usually clustered into structures called cones—for example, pine cones. By contrast the seed of angiosperms is enclosed in a ripened ovary, the fruit. See also Magnoliophyta; Pinophyta; Polypodiales; Tree ferns.
The orders Cycadales, Ginkgoales, and Pinales of the Pinophyta contain trees. Ginkgo biloba, the ancient maidenhair tree, is the single present-day member of the Ginkgoales. The Cycadales, characteristic of dry tropical areas, contain many species which are small trees. The Pinales, found throughout the world, supply much of the wood, paper, and building products of commerce. They populate at least one-third of all existing forest and include the pines (Pinus), hemlocks (Tsuga), cedars (Cedrus), spruces (Picea), firs (Abies), cypress (Cupressus), larches (Larix), Douglas-fir (Pseudotsuga), sequoia (Sequoia), and other important genera. The Pinales are known in the lumber trade as softwoods and are popularly thought of as evergreens, although some (for example, larch and bald cypress) shed their leaves in the winter. See also Cedar; Cycadales; Cypress; Douglas-fir; Fir; Hemlock; Larch; Paper; Pinales; Pine; Pinophyta; Sequoia; Spruce.
In contrast to the major orders of gymnosperms which contain only trees, many angiosperm families are herbaceous and include trees only as an exception. Only a few are exclusively arborescent. The major classes of the angiosperms are the Liliopsida (monocotyledons) and the Magnoliopsida (dicotyledons). The angiosperm trees, commonly thought of as broad-leaved and known as hardwoods in the lumber market, are dicotyledons. Examples of important genera are the oaks (Quercus), elms (Ulmus), maples (Acer), and poplars (Populus). See also Elm; Liliopsida; Magnoliopsida; Maple; Oak; Poplar.
The Liliopsida contain few tree species, and these are never used for wood products, except in the round as posts. Examples of monocotyledonous families are the palms (Palmae), yucca (Liliaceae), bamboos (Bambusoideae), and bananas (Musaceae). See also Bamboo; Banana.
Morphology
The morphology of a tree is similar to that of other higher plants. Its major organs are the stem, or trunk and branches; the leaves; the roots; and the reproductive structures. Almost the entire bulk of a tree is nonliving. Of the trunk, branches, and roots, only the tips and a thin layer of cells just under the bark are alive. Growth occurs only in these meristematic tissues. Meristematic cells are undifferentiated and capable of repeated division. See also Flower; Lateral meristem; Leaf; Plant growth; Root (botany); Stem.
Growth
Height is a result of growth only in apical meristems at the very tips of the twigs. A nail driven into a tree will always remain at the same height, and a branch which originates from a bud at a given height will never rise higher. The crown of a tree ascends as a tree ages only by the production of new branches at the top and by the death and abscission of lower, older branches as they become progressively more shaded. New growing points originate from the division of the apical meristem and appear as buds in the axils of leaves. See also Apical meristem; Bud; Plant growth.
In the gymnosperms and the dicotyledonous angiosperms, growth in diameter occurs by division in only a single microscopic layer, three or four cells wide, which completely encircles and sheaths the tree. This lateral meristem is the cambium. It divides to produce xylem cells (wood) on the inside toward the core of the tree and phloem cells on the outside toward the bark. In trees of the temperate regions the growth of each year is seen in cross section as a ring. See also Bark; Phloem; Xylem.
Xylem elements become rigid through the thickening and modification of their cell wall material. The tubelike xylem cells transport water and nutrients from the root through the stem to the leaves. In time the xylem toward the center of the trunk becomes impregnated with various mineral and metabolic products, and it is no longer capable of conduction. This nonfunctional xylem is called heartwood and is recognizable in some stems by its dark color. The light-colored, functional outer layer of the xylem is the sapwood. See also Wood anatomy.
The phloem tissue transports dissolved carbohydrates and other metabolic products manufactured by the leaves throughout the stem and the roots. Most of the phloem cells are thin-walled and are eventually crushed between the bark and the cambium by the pressures generated in growth. The outer bark is dead and inelastic but the inner bark contains patches of cork cambium which produce new bark. As a tree increases in circumference, the old outer bark splits and fissures develop, resulting in the rough appearance characteristic of the trunks of most large trees.
In the monocotyledons the lateral cambium does not encircle a central core, and the vascular or conducting tissue is organized in bundles scattered throughout the stem. The trunk is not wood as generally conceived although it does in fact have secondary xylem. See also Dendrology; Forest and forestry; Plant physiology; Plant taxonomy.
| Computer Desktop Encyclopedia: tree |
A hierarchical structure such as the organization of a company. The term is derived from the concept of tree branches. For example, in a company organization chart, the top of the tree is the starting point, or highest level, such as the executive office. Various departments are branches that stem from the highest level, with smaller sections branching off the departments.
Files and Folders and the Root
The term often refers to the file/folder hierarchy of a hard disk. In Windows, the Explorer utility is used to display these hierarchies, while Finder provides the same view in the Mac. In an application, menu options such as "view directory," "directory tree," "view tree" or simply "tree" also display the hierarchy.
The very top of a file/folder hierarchy is called the "root," even though the roots of a real tree are at the bottom in the earth. The file/folder tree is conceptualized as a real tree upside down. See root and forests and trees.
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| Abbreviations: TREE |
| Meaning | Category |
| Lending Tree, Inc. | Business->NASDAQ Symbols |
| Teach Responsibility, Empower, and Educate | Community->Educational |
| Trends in Ecology & Evolution | Academic & Science->Universities |
| Tropical Rainforest Ecology Experiment | Academic & Science->Ocean Science |
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| Wikipedia: Tree (graph theory) |
| Trees | |
 A labeled tree with 6 vertices and 5 edges |
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| Vertices | v |
|---|---|
| Edges | v - 1 |
| Chromatic number | 2 |
In mathematics, more specifically graph theory, a tree is a graph in which any two vertices are connected by exactly one path. In other words, any connected graph without cycles is a tree. A forest is a disjoint union of trees.
The various kinds of trees used as data structures in computer science are not really trees in this sense, but rather, types of ordered directed trees; see below.
Contents |
Definitions
A tree is an undirected simple graph G that satisfies any of the following equivalent conditions:
- G is connected and has no cycles.
- G has no cycles, and a simple cycle is formed if any edge is added to G.
- G is connected, and it is not connected anymore if any edge is removed from G.
- G is connected and the 3-vertex complete graph K3 is not a minor of G.
- Any two vertices in G can be connected by a unique simple path.
If G has finitely many vertices, say n of them, then the above statements are also equivalent to any of the following conditions:
- G is connected and has n − 1 edges.
- G has no simple cycles and has n − 1 edges.
An irreducible (or series-reduced) tree is a tree in which there is no vertex of degree 2.
An undirected simple graph G is called a forest if it has no simple cycles.
The term hedge sometimes refers to an ordered sequence of trees.
A polytree is a directed graph with at most one undirected path between any two vertices. In other words, a polytree is a directed acyclic graph for which there are no undirected cycles either.
A directed tree is a directed graph which would be a tree if the directions on the edges were ignored. Some authors restrict the phrase to the case where the edges are all directed towards a particular vertex, or all directed away from a particular vertex (see arborescence.)
A tree is called a rooted tree if one vertex has been designated the root, in which case the edges have a natural orientation, towards or away from the root. The tree-order is the partial ordering on the vertices of a tree with u ≤ v if and only if the unique path from the root to v passes through u. A tree which is a subgraph of some graph G is a normal tree if the ends of every edge in G are comparable in this tree-order (Diestel 2005, p. 15). Rooted trees, often with additional structure such as ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure. In a context where trees are supposed to have a root, a tree without any designated root is called a free tree.
In a rooted tree, the parent of a vertex is the vertex connected to it on the path to the root; every vertex except the root has a unique parent. A child of a vertex v is a vertex of which v is the parent. A leaf is a vertex without children.
A labeled tree is a tree in which each vertex is given a unique label. The vertices of a labeled tree on n vertices are typically given the labels 1, 2, …, n. A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v, then the label of u is smaller than the label of v).
An ordered tree is a rooted tree for which an ordering is specified for the children of each vertex.
An n-ary tree is a rooted tree for which each vertex which is not a leaf has at most n children. 2-ary trees (resp. 3-ary trees) are sometimes called binary trees (resp. ternary trees)
Example
The example tree shown to the right has 6 vertices and 6 − 1 = 5 edges. The unique simple path connecting the vertices 2 and 6 is 2-4-5-6.
Facts
- Every tree is a bipartite graph and a median graph. Every tree with only countably many vertices is a planar graph.
- Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G. Every connected graph even admits a normal spanning tree (Diestel 2005, Prop. 1.5.6).
- Every finite tree with at least two vertices, say n, has at least two leaves or vertices of degree 1. The minimal number of leaves corresponds to the path graph and the maximal number (n - 1) corresponds to the star graph.
- For any three vertices in a tree, the three paths between them have at least one vertex in common.
Enumeration
Given n labeled vertices, there are nn−2 different ways to connect them to make a tree. This result is called Cayley's formula. It can be proved by first showing that the number of trees with n vertices of degree d1,d2,...,dn is the multinomial coefficient
An alternative proof uses Prüfer sequences.
Counting the number of unlabeled trees is a harder problem. No closed formula for the number t(n) of trees with n vertices up to graph isomorphism is known. Otter (1948) proved that
with C = 0.53495… and α = 2.95576… (here, 
means that 
).
Types of trees
See also
References
- Diestel, Reinhard (2005), Graph Theory (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-26183-4, http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/.
- Otter, Richard (1948), "The Number of Trees", Annals of Mathematics, Second Series 49 (3): 583–599, doi:.
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