Rooted graph
Encyclopedia
In mathematics
, and, in particular, in graph theory
, a rooted graph is a mathematical graph
in which one node is labelled in a special way to distinguish it from the graph's other nodes. This special node is called the root of the graph.
The number of rooted graphs for 1, 2, ... nodes is 1, 2, 6, 20, 90, 544, ...
A special case of interest are rooted trees.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, and, in particular, in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, a rooted graph is a mathematical graph
Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
in which one node is labelled in a special way to distinguish it from the graph's other nodes. This special node is called the root of the graph.
The number of rooted graphs for 1, 2, ... nodes is 1, 2, 6, 20, 90, 544, ...
A special case of interest are rooted trees.