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Graph polynomial. In mathematics, a graph polynomial is a graph invariant whose value is a polynomial. Invariants of this type are studied in algebraic graph theory. [1] Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. The chromatic polynomial, a polynomial whose values at integer ...
The graph of a polynomial function of degree 3. The x occurring in a polynomial is commonly called a variable or an indeterminate. When the polynomial is considered as an expression, x is a fixed symbol which does not have any value (its value is "indeterminate").
The graph of a univariate quadratic function is a parabola, a curve that has an axis of symmetry parallel to the y -axis. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros of the corresponding quadratic function. The bivariate case in terms of variables x ...
Chromatic polynomial. All non-isomorphic graphs on 3 vertices and their chromatic polynomials, clockwise from the top. The independent 3-set: k3. An edge and a single vertex: k2(k – 1). The 3-path: k(k – 1)2. The 3-clique: k(k – 1) (k – 2). The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of ...
Matching polynomial. Appearance. hide. In the mathematical fields of graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory .
The polynomial is the Tutte polynomial of the bull graph. The red line shows the intersection with the plane , which is essentially equivalent to the chromatic polynomial. The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role ...
Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4. In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex ...
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). If the slope is , this is a constant function defining a ...