In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems.The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs).The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time. Boundaries between tractable and intractable cases have been an active area of research. (Wikipedia).
Graph Theory FAQs: 04. Isomorphism vs Homomorphism
In this video we recall the definition of a graph isomorphism and then give the definition of a graph homomorphism. Then we look at two examples of graph homomorphisms and discuss a special case that relates to graph colourings. -- Graph Theory FAQs by Dr. Sarada Herke. Related videos:
From playlist Graph Theory FAQs
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Graph Theory FAQs: 02. Graph Automorphisms
An automorphism of a graph G is an isomorphism between G and itself. The set of automorphisms of a graph forms a group under the operation of composition and is denoted Aut(G). The automorphisms of a graph describe the symmetries of the graph. We look at a few examples of graphs and det
From playlist Graph Theory FAQs
This video defines and gives and example of isomorphic graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Homomorphisms in abstract algebra examples
Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th
From playlist Abstract algebra
4a Isomorphism of Graphs (brief)
From playlist Graph Theory
Group Homomorphisms - Abstract Algebra
A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be
From playlist Abstract Algebra
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)
From playlist Abstract Algebra
14. Graph limits I: introduction
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Graph limits provide a beautiful analytic framework for s
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Graph Density Inequalities, Sums of Squares and Tropicalization - Annie Raymond
Computer Science/Discrete Mathematics Seminar I Topic: Graph Density Inequalities, Sums of Squares and Tropicalization Speaker: Annie Raymond Affiliation: University of Massachusetts Amherst Date: February 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Graph Theory: Isomorphisms and Connectedness
This video is about isomorphisms between graphs and connectedness of graphs.
From playlist Basics: Graph Theory
J. Aramayona - MCG and infinite MCG (Part 3)
The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the secon
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Sparse Graph Limits 1: Left and Right convergence - Jennifer Chayes
Conference on Graphs and Analysis Jennifer Chayes June 6, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Volodymyr Nekrashevych: Contracting self-similar groups and conformal dimension
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'
From playlist Dynamical Systems and Ordinary Differential Equations
Ben Knudsen (7/28/22): The topological complexity of pure graph braid groups is stably maximal
I will discuss a proof of Farber's conjecture on the topological complexity of configuration spaces of graphs. The argument eschews cohomology, relying instead on group theoretic estimates for higher topological complexity due to Farber–Oprea following Grant–Lupton–Oprea.
From playlist Topological Complexity Seminar
Stability and sofic approximations for product groups and property (tau) - Adrian Ioana
Stability and Testability Topic: Stability and sofic approximations for product groups and property (tau) Speaker: Adrian Ioana Affiliation: University of California, San Diego Date: November 4, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Danny Calegari: Big Mapping Class Groups - lecture 3
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h
From playlist Topology
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - V.Paulsen
Vern Paulsen (Waterloo) / 12.09.17 Title: C*-algebras and Synchronous Games. Abstract: In recent years a deep connection has been found between Connnes’ embedding problem and Tsirelson’s questions about various sets of probabilistic quantum correlations, called local, quantum, quantum a
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra