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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.
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.
A root of a polynomial is a zero of the corresponding polynomial function. [1] The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree , and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically ...
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),
The graph of the function f(x) = √x, made up of half a parabola with a vertical directrix. The principal square root function () = (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself.
If the parabola is tangent to the x-axis, there is a double root, which is the x-coordinate of the contact point between the graph and parabola. If the parabola does not intersect the x-axis, there are two complex conjugate roots. Although these roots cannot be visualized on the graph, their real and imaginary parts can be. [17]
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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