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In the mathematical field of graph theory, the intersection number of a graph = (,) is the smallest number of elements in a representation of as an intersection graph of finite sets. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element.
5. The intersection number of arbitrary divisors is then defined using a "Chow's moving lemma" that guarantees we can find linearly equivalent divisors that are in general position, which we can then intersect. Note that the definition of the intersection number does not depend on the order in which the divisors appear in the computation of ...
The line graph of a graph G is defined as the intersection graph of the edges of G, where we represent each edge as the set of its two endpoints. A string graph is the intersection graph of curves on a plane. A graph has boxicity k if it is the intersection graph of multidimensional boxes of dimension k, but not of any smaller dimension.
graph intersection: G 1 ∩ G 2 = (V 1 ∩ V 2, E 1 ∩ E 2); [1] graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets: cartesian graph product: it is a ...
So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist. However, when restricted to the context of subsets of a given fixed set X {\displaystyle X} , the notion of the intersection of an empty collection of ...
This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle C with center E. [5] This proves that the intersection of P and S is contained in C. Note that OE is the axis of the circle. Now consider a point D of the circle C. Since C lies in ...
P n [1] Table of graphs and parameters In the mathematical field of graph theory , a path graph (or linear graph ) is a graph whose vertices can be listed in the order v 1 , v 2 , ..., v n such that the edges are { v i , v i +1 } where i = 1, 2, ..., n − 1 .
An intersection graph of rectangles, with boxicity two. In graph theory, boxicity is a graph invariant, introduced by Fred S. Roberts in 1969.. The boxicity of a graph is the minimum dimension in which a given graph can be represented as an intersection graph of axis-parallel boxes.