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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.
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 ...
These are the three vertices A such that d(A, B) ≤ 3 for all vertices B. Each black vertex is a distance of at least 4 from some other vertex. The center (or Jordan center [1]) of a graph is the set of all vertices of minimum eccentricity, [2] that is, the set of all vertices u where the greatest distance d(u,v) to other vertices v is
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
These are seen as the vertices of the vertex figure. Related to the vertex figure, an edge figure is the vertex figure of a vertex figure. [3] Edge figures are useful for expressing relations between the elements within regular and uniform polytopes. An edge figure will be a (n−2)-polytope, representing the arrangement of facets around a ...
The complete graph on n vertices is denoted by K n.Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.
A d-claw in a graph is a set of d+1 vertices, one of which (the "center") is connected to the other d vertices, but the other d vertices are not connected to each other. A d-claw-free graph is a graph that does not have a d-claw subgraph. Consider the algorithm that starts with an empty set, and incrementally adds an arbitrary vertex to it as ...
In the limit, these approach a curve that traces out the Sierpiński triangle by a single continuous directed (infinitely wiggly) path, which is called the Sierpiński arrowhead. [5] In fact, the aim of Sierpiński's original article in 1915 was to show an example of a curve (a Cantorian curve), as the title of the article itself declares.