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Unrooted binary tree : ウィキペディア英語版
Unrooted binary tree

In mathematics and computer science, an unrooted binary tree is an unrooted tree in which each vertex has either one or three neighbors.
==Definitions==
A free tree or unrooted tree is a connected undirected graph with no cycles. The vertices with one neighbor are the ''leaves'' of the tree, and the remaining vertices are the ''internal nodes'' of the tree. The degree of a vertex is its number of neighbors; in a tree with more than one node, the leaves are the vertices of degree one. An unrooted binary tree is a free tree in which all internal nodes have degree exactly three.
In some applications it may make sense to distinguish subtypes of unrooted binary trees: a planar embedding of the tree may be fixed by specifying a cyclic ordering for the edges at each vertex, making it into a plane tree. In computer science, binary trees are often rooted and ordered when they are used as data structures, but in the applications of unrooted binary trees in hierarchical clustering and evolutionary tree reconstruction, unordered trees are more common.〔
Additionally, one may distinguish between trees in which all vertices have distinct labels, trees in which the leaves only are labeled, and trees in which the nodes are not labeled. In an unrooted binary tree with ''n'' leaves, there will be ''n'' − 2 internal nodes, so the labels may be taken from the set of integers from 1 to 2''n'' − 1 when all nodes are to be labeled, or from the set of integers from 1 to ''n'' when only the leaves are to be labeled.〔.〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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