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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
A vertex with a large degree, also called a heavy node, results in a large diagonal entry in the Laplacian matrix dominating the matrix properties. Normalization is aimed to make the influence of such vertices more equal to that of other vertices, by dividing the entries of the Laplacian matrix by the vertex degrees.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
A directed graph with three vertices (blue circles) and three edges (black arrows).. In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics.
2-colour case proof without words. Due to the pigeonhole principle, there are at least 3 edges of the same colour (dashed purple) from an arbitrary vertex v.Calling 3 of the vertices terminating these edges r, s and t, if the edge rs, st or tr (solid black) had this colour, it would complete the triangle with v.
A cycloid generated by a rolling circle. In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve.
Insertion of a point may increase the number of vertices of a convex hull at most by 1, while deletion may convert an n-vertex convex hull into an n-1-vertex one. The online version may be handled with O(log n) per point, which is asymptotically optimal. The dynamic version may be handled with O(log 2 n) per operation. [1]
If a line l goes from vertex v to vertex v′, then M(l) goes from N(v) to N(v′). If the line is undirected, as it is for a real scalar field, then M(l) can go from N(v′) to N(v) too. If a line l ends on an external line, M(l) ends on the same external line. If there are different types of lines, M(l) should preserve the type.