Graph invariants | Polynomials

Graph polynomial

In mathematics, a graph polynomial is a graph invariant whose values are polynomials. Invariants of this type are studied in algebraic graph theory.Important graph polynomials include: * The characteristic polynomial, based on the graph's adjacency matrix. * The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. * The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial * The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts modulo the argument. * The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. * The , used by Pierre Martin to study Euler tours * The matching polynomials, several different polynomials defined as the generating function of the matchings of a graph. * The reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures * The Tutte polynomial, a polynomial in two variables that can be defined (after a small change of variables) as the generating function of the numbers of connected components of induced subgraphs of the given graph, parameterized by the number of vertices in the subgraph. (Wikipedia).

Video thumbnail

Graph the polynomial given polynomial and using multiplicity and end behavior

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Sketching the graph of a polynomial using the zeros and multiplicity

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Sketch the graph of the polynomial by hand using zeros, multiplicity and end behavior

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Zeros, graphing, multiplicity polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Sketch the graph of a factored polynomial using multiplicity

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Determine the multiplicity and zeros and graph of a polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

How to use the zeros and multiplicity to graph the equation of a polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Using multiplicity to help us sketch the graph of a polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Given the zeros, find the end behavior to sketch the graph of a polynomial

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Video thumbnail

Watch how easy it is to sketch a polynomial graph y = (x + 3)(x – 2)(x + 1)

How to sketch the graph of a polynomial. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All co

From playlist Pre-Calculus / Trigonometry

Video thumbnail

Ramanujan graphs of every degree - Daniel Spielman

Daniel Spielman Yale University November 6, 2014 We explain what Ramanujan graphs are, and prove that there exist infinite families of bipartite Ramanujan graphs of every degree. Our proof follows a plan suggested by Bilu and Linial, and exploits a proof of a conjecture of theirs about li

From playlist Mathematics

Video thumbnail

Polynomials – The BIG PICTURE…you need know….

TabletClass Math: https://tcmathacademy.com/ Math help with polynomials to include graphs and how to find roots. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebr

From playlist Pre-Calculus / Trigonometry

Video thumbnail

X-Ramanujan graphs: ex uno plures - Ryan O'Donnell

Computer Science/Discrete Mathematics Seminar Topic: X-Ramanujan graphs: ex uno plures Speaker: Ryan O'Donnell Affiliation: Carnegie Mellon University Time/Room: 3:30pm - 4:30pm/Simonyi Hall 101 Date: October 29, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Loïc FOISSY - Cointeracting Bialgebras

Pairs of cointeracting bialgebras recently appears in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, Manchon), graphs (Manchon), posets... We will give several results obtained on pairs of cointeracting bialgebras: act

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Video thumbnail

Elise Goujard: Volumes of odd strata of quadratic differentials

CONFERENCE Recording during the thematic meeting : "Combinatorics, Dynamics and Geometry on Moduli Spaces" the September 20, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwid

From playlist Combinatorics

Video thumbnail

Episode 7: Polynomials - Project MATHEMATICS!

Episode 7. Polynomials: Animation shows how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Real-life examples include parabolic trajectories and the use of c

From playlist Courses and Series

Video thumbnail

Saliency + Combinatorial Invariance: Geordie Williamson

Machine Learning for the Working Mathematician: Week Six 31 March 2022 Geordie Williamson, Saliency + an application: combinatorial invariance Seminar series homepage (includes Zoom link): https://sites.google.com/view/mlwm-seminar-2022

From playlist Machine Learning for the Working Mathematician

Video thumbnail

Polynomial Graphs Part 1

I introduce polynomial functions and give examples of what their graphs may look like. I then go over how to determine the End Behavior of these graphs. Part 2 will include finding y-intercepts, x-intercepts and their multiplicity, determining even or odd, and sketching the function. At

From playlist PreCalculus

Video thumbnail

How to Graph a Polynomial

TabletClass Math http://www.tabletclass.com complete courses in middle and high school math. Perfect for homeschoolers and those that want to learn math on their own. This video explains how to graph a polynomial function. High school algebra 1 and algebra 2 students will find this video

From playlist Algebra 2

Video thumbnail

How to sketch the graph of a polynomial by zeros and multiplicity

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh

From playlist Graph a Polynomial Function in Factored Form

Related pages

Polynomial | Adjacency matrix | Graph property | Induced subgraph | Knot polynomial | Matching polynomial | Nowhere-zero flow | Characteristic polynomial | Chromatic polynomial | Matching (graph theory) | Algebraic graph theory | Ihara zeta function | Generating function | Tutte polynomial