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In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. [ 1 ] [ 2 ] Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots.
The rooted product of graphs. In mathematical graph theory, the rooted product of a graph G and a rooted graph H is defined as follows: take | V(G) | copies of H, and for every vertex v i of G, identify v i with the root node of the i-th copy of H. More formally, assuming that
A path graph (or linear graph) consists of n vertices arranged in a line, so that vertices i and i + 1 are connected by an edge for i = 1, …, n – 1. A starlike tree consists of a central vertex called root and several path graphs attached to it. More formally, a tree is starlike if it has exactly one vertex of degree greater than 2.
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), [6] with a distinguished root (one vertex is designated as the root),
An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.
In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly one directed walk from r to v (noting that the root r is unique). [1] An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph.
A graph is d-regular when all of its vertices have degree d. A regular graph is a graph that is d-regular for some d. regular tournament A regular tournament is a tournament where in-degree equals out-degree for all vertices. reverse See transpose. root 1. A designated vertex in a graph, particularly in directed trees and rooted graphs. 2.
The numbers beside the vertices indicate the distance from the root vertex. In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G.