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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 ...
A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]
A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.
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).
In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. [1] Formally, given a graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph.
All complete graphs are their own maximal cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament.
Vertex (geometry), a point where two or more curves, lines, or edges meet; Vertex (computer graphics), a data structure that describes the position of a point; Vertex (curve), a point of a plane curve where the first derivative of curvature is zero; Vertex (graph theory), the fundamental unit of which graphs are formed
In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. [1] This is typically a local maximum or minimum of curvature, [ 2 ] and some authors define a vertex to be more specifically a local extremum of curvature. [ 3 ]