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A vertex (plural vertices) in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space, or multiple points on a surface. Application to 3D models
Basically, a 3D model is formed from points called vertices that define the shape and form polygons. A polygon is an area formed from at least three vertices (a triangle). A polygon of n points is an n-gon. [10] The overall integrity of the model and its suitability to use in animation depend on the structure of the polygons.
A unit distance graph with 16 vertices and 40 edges. In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one.
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).
A "harmonious labeling" on a graph G is an injection from the vertices of G to the group of integers modulo k, where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge (x, y) to be the sum of the labels of the two vertices x, y (mod k). A "harmonious graph ...
This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. Alternative representation of the hypergraph reported in the figure above, called PAOH. [1] Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left.
An independent set of ⌊ ⌋ vertices (where ⌊ ⌋ is the floor function) in an n-vertex triangle-free graph is easy to find: either there is a vertex with at least ⌊ ⌋ neighbors (in which case those neighbors are an independent set) or all vertices have strictly less than ⌊ ⌋ neighbors (in which case any maximal independent set must have at least ⌊ ⌋ vertices). [4]
For a graph with n vertices, h of which are fixed in position on the outer face, there are two equations for each interior vertex and also two unknowns (the coordinates) for each interior vertex. Therefore, this gives a system of linear equations with 2( n − h ) equations in 2( n − h ) unknowns, the solution to which is a Tutte embedding.