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v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...
Rooted graph. 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. Rooted graphs may also be known (depending on ...
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
Graph traversal. In computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals are classified by the order in which the vertices are visited. Tree traversal is a special case of graph traversal.
separation number Vertex separation number is a synonym for pathwidth. sibling In a rooted tree, a sibling of a vertex v is a vertex which has the same parent vertex as v. simple 1. A simple graph is a graph without loops and without multiple adjacencies. That is, each edge connects two distinct endpoints and no two edges have the same endpoints.
Once a vertex is marked as the root, we can group the other vertices into layers based on their distance from the root. The number of vertices at a distance > from the root is (), as each vertex other than the root is adjacent to vertices at a distance one greater from the root, and the root is adjacent to vertices at a distance 1.
Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange). Its x-intercepts are rotated 90° around their mid-point, and the Cartesian plane is interpreted as the complex plane (green). [3
Arborescence (graph theory) 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 ...