View source for Tree (graph theory)

In [[mathematics]], and more specifically in [[graph theory]], a '''tree''' is an [[undirected graph]] in which any two [[vertices]] are connected by exactly one [[path]].

== Description ==

In other words, any connected graph without simple cycles is a tree.

A [[forest]] is a [[disjoint union]] of trees.

== Rooted Trees ==

The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees, thus in fact being directed graphs, and may also have additional ordering of branches.

Rooted trees in their directed graph form may be called [[Directed root tree|directed rooted trees]].

Other terms for this include arborescence, out-arborescence, out-tree, and even branching.

== History ==

The term "tree" was coined in 1857 by the British mathematician [[Arthur Cayley]].

== See also ==

* [[Analogy]]
* [[Graph theory]]
* [[Mathematics]]
* [[Tree (computer science)]]

== External links == 

* [https://en.wikipedia.org/wiki/Tree_(graph_theory) Tree (graph theory)] @ Wikipedia