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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
Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, Jordan (1869) has proved that for trees, there are only two possibilities: The tree has precisely one center (centered ...
This yields the center as given below. An alternative approach that uses the matrix form of the quadratic equation is based on the fact that when the center is the origin of the coordinate system, there are no linear terms in the equation. Any translation to a coordinate origin (x 0, y 0), using x* = x – x 0, y* = y − y 0 gives rise to
In geometry, focuses or foci (/ ˈ f oʊ k aɪ /; sg.: focus) are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola.
The linear eccentricity of an ellipse or hyperbola, denoted c (or sometimes f or e), is the distance between its center and either of its two foci. The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a : that is, e = c a {\displaystyle e={\frac {c}{a}}} (lacking a center, the linear eccentricity for ...
A,C: vertices of the ellipse and foci of the hyperbola E,F: foci of the ellipse and vertices of the hyperbola Focal conics: two parabolas A: vertex of the red parabola and focus of the blue parabola F: focus of the red parabola and vertex of the blue parabola. In geometry, focal conics are a pair of curves consisting of [1] [2] either
The midpoint of the line segment joining the foci is called the center of the hyperbola. [6] The line through the foci is called the major axis . It contains the vertices V 1 , V 2 {\displaystyle V_{1},V_{2}} , which have distance a {\displaystyle a} to the center.
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 ...