rooted tree

In graph theory, a tree is a type of graph that contains no cycles. A rooted tree is a tree where one vertex, known as the root, is distinguished from all other vertices. This root serves as a starting point for analyzing the tree's structure. The number of labeled trees with v vertices is v^v-2, a result first shown by Cayley. The enumeration of unlabelled trees and rooted trees can be determined using advanced mathematical theorems, such as Polya's theorem. While the term "root" also refers to the underground part of a plant that anchors it and absorbs nutrients, in graph theory, it signifies a specific designated vertex within a tree structure.123