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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. Examples of rooted graphs with some variants.
Every connected graph in which the domination number is half the number of vertices arises in this way, with the exception of the four-vertex cycle graph. These graphs can be used to generate examples in which the bound of Vizing's conjecture , an unproven inequality between the domination number of the graphs in a different graph product, the ...
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),
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
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.
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
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.