Assertion: rooted tree | /r/HasProperty | arborescence
Facets:
value: equivalently
type: DEGREE
Source sentences:
text: A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple path), with a distinguished root (one vertex is designated as the root), which determines the direction on the edges (arrows point away from the root; given an edge, the node that the edge points from is called the parent and the node that the edge points to is called the child ),
text: 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.
text: The necessary distinction can be made by first partitioning the edges, i.e., defining the binary tree as triplet (V, E 1 , E 2 ), where (V, E 1 ∪ E 2 ) is a rooted tree (equivalently arborescence) and E 1 ∩ E 2 is empty, and also requiring that for all j ∈ { 1, 2 } every node has at most one E j child.
text: When a directed rooted tree has an orientation away from the root, it is called an arborescence or out-tree; when it has an orientation towards the root, it is called an anti-arborescence or in-tree.