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A special case of interest are rooted trees, the trees with a distinguished root vertex. If the directed paths from the root in the rooted digraph are additionally restricted to be unique, then the notion obtained is that of (rooted) arborescence—the directed-graph equivalent of a rooted tree. [7]
When a directed rooted tree has an orientation away from the root, it is called an arborescence [3] or out-tree; [11] when it has an orientation towards the root, it is called an anti-arborescence or in-tree. [11] 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 ...
A rooted phylogenetic tree (see two graphics at top) is a directed tree with a unique node — the root — corresponding to the (usually imputed) most recent common ancestor of all the entities at the leaves of the tree. The root node does not have a parent node, but serves as the parent of all other nodes in the tree.
The tree decomposition of a graph is far from unique; for example, a trivial tree decomposition contains all vertices of the graph in its single root node. A tree decomposition in which the underlying tree is a path graph is called a path decomposition, and the width parameter derived from these special types of tree decompositions is known as ...
Edward Hitchcock's fold-out paleontological chart in his 1840 Elementary Geology. Although tree-like diagrams have long been used to organise knowledge, and although branching diagrams known as claves ("keys") were omnipresent in eighteenth-century natural history, it appears that the earliest tree diagram of natural order was the 1801 "Arbre botanique" (Botanical Tree) of the French ...
An unrooted binary tree T may be transformed into a full rooted binary tree (that is, a rooted tree in which each non-leaf node has exactly two children) by choosing a root edge e of T, placing a new root node in the middle of e, and directing every edge of the resulting subdivided tree away from the root node. Conversely, any full rooted ...
A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.
The original tree is converted to a binary tree: each node with more than two children is replaced by a sub-tree in which each node has exactly two children. Each region representing a node (starting from the root) is divided to two, using a line that keeps the angles between edges as large as possible.