Wurzelbäumen
Wurzelbäumen (German for "rooted trees") are trees in graph theory and computer science that have a distinguished vertex called the root. Each edge implicitly orients away from the root, establishing parent–child relationships that define ancestors, descendants, leaves (vertices with no children), depth (distance from the root) and height (maximum depth). Rooted trees may be ordered (children have a left-to-right sequence) or unordered, and may be labeled or unlabeled; common special cases include binary trees and k-ary trees.
In combinatorics and enumeration, rooted trees are a central object. Cayley’s formula counts labeled trees on
In computer science, rooted trees model hierarchical data and enable efficient algorithms: syntax trees and abstract
The study of rooted trees intersects graph theory, combinatorics, algorithm design and applications across disciplines, providing