Search results
Results from the WOW.Com Content Network
The degree sequence of an undirected graph is the non-increasing sequence of its vertex degrees; [5] for the above graph it is (5, 3, 3, 2, 2, 1, 0). The degree sequence is a graph invariant, so isomorphic graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a graph; in some cases, non ...
One proof of this involves approximating the function by a piecewise linear function with the same extreme points, parameterizing the position of the two moving points by the coordinates of a single point in the unit square, and showing that the available positions for the two points form a finite graph, embedded in this square, with only the ...
The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
As the integrand is the polynomial of degree 3 (y(x) = 7x 3 – 8x 2 – 3x + 3), the 2-point Gaussian quadrature rule even returns an exact result. In numerical analysis , an n -point Gaussian quadrature rule , named after Carl Friedrich Gauss , [ 1 ] is a quadrature rule constructed to yield an exact result for polynomials of degree 2 n − 1 ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...