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A vertex can reach a vertex (and is reachable from ) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with and ends with . In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph.
In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edges so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face (or ...
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity. Formally, an automorphism of a graph G = ( V , E ) is a permutation σ of the vertex set V , such that the pair of vertices ( u , v ) form an edge if and only if ...
A cutpoint, cut vertex, or articulation point of a graph G is a vertex that is shared by two or more blocks. The structure of the blocks and cutpoints of a connected graph can be described by a tree called the block-cut tree or BC-tree. This tree has a vertex for each block and for each articulation point of the given graph.
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 ...
In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of . In linear programming problems, an extreme point is also called vertex or corner point of S . {\displaystyle S.} [ 1 ]
A vertex configuration can also be represented as a polygonal vertex figure showing the faces around the vertex. This vertex figure has a 3-dimensional structure since the faces are not in the same plane for polyhedra, but for vertex-uniform polyhedra all the neighboring vertices are in the same plane and so this plane projection can be used to visually represent the vertex configuration.
separating vertex See articulation point. 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 ...