Search results
Results from the WOW.Com Content Network
An ordered pair of vertices, such as an edge in a directed graph. An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would ...
The Keynesian cross diagram includes an identity line to show states in which aggregate demand equals output. In a 2-dimensional Cartesian coordinate system, with x representing the abscissa and y the ordinate, the identity line [1] [2] or line of equality [3] is the y = x line. The line, sometimes called the 1:1 line, has a slope of 1. [4]
A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. [2] For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m. [6]
In set theory and graph theory, denotes the set of n-tuples of elements of , that is, ordered sequences of elements that are not necessarily distinct. In the edge ( x , y ) {\displaystyle (x,y)} directed from x {\displaystyle x} to y {\displaystyle y} , the vertices x {\displaystyle x} and y {\displaystyle y} are called the endpoints of the ...
Oriented graphs are directed graphs having no opposite pairs of directed edges (i.e. at most one of (x, y) and (y, x) may be arrows of the graph). It follows that a directed graph is an oriented graph if and only if it has no 2-cycle. [6] Such a graph can be obtained by applying an orientation to an undirected graph.
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 ...
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:
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.