Tree (mathematics) | Wikipedia audio article

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00:00:47 1 Definitions
00:01:11 1.1 Tree
00:01:59 1.2 Forest
00:02:47 1.3 Polytree
00:03:35 1.4 Polyforest
00:04:23 1.5 Rooted tree
00:05:11 1.6 Ordered tree
00:05:59 2 Properties
00:06:47 3 Enumeration
00:07:35 3.1 Labeled trees
00:07:59 3.2 Unlabeled trees
00:08:46 4 Types of trees
00:09:34 5 See also
00:10:22 6 Notes



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SUMMARY
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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest.
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. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence or out-tree—or making all its edges point towards the root—in which case it is called an anti-arborescence or in-tree. A rooted tree itself has been defined by some authors as a directed graph. A rooted forest is a disjoint union of rooted trees. A rooted forest may be directed, called a directed rooted forest, either making all its edges point away from the root in each rooted tree—in which case it is called a branching or out-forest—or making all its edges point towards the root in each rooted tree—in which case it is called an anti-branching or in-forest.
The term "tree" was coined in 1857 by the British mathematician Arthur Cayley.