Morphisms | Graph algorithms | Graph theory
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection.If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as . In the case when the bijection is a mapping of a graph onto itself, i.e., when G and H are one and the same graph, the bijection is called an automorphism of G.If a graph is finite, we can prove it to be bijective by showing it is one-one/onto; no need to show both. Graph isomorphism is an equivalence relation on graphs and as such it partitions the class of all graphs into equivalence classes. A set of graphs isomorphic to each other is called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer science. The two graphs shown below are isomorphic, despite their different looking drawings. (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
This video defines and gives and example of isomorphic graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Theory: 09. Graph Isomorphisms
In this video I provide the definition of what it means for two graphs to be isomorphic. I illustrate this with two isomorphic graphs by giving an isomorphism between them, and conclude by discussing what it means for a mapping to be a bijection. An introduction to Graph Theory by Dr. Sar
From playlist Graph Theory part-2
4a Isomorphism of Graphs (brief)
From playlist Graph Theory
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
Graph Theory: Isomorphisms and Connectedness
This video is about isomorphisms between graphs and connectedness of graphs.
From playlist Basics: Graph Theory
What are Isomorphic Graphs? | Graph Isomorphism, Graph Theory
How do we formally describe two graphs "having the same structure"? The term for this is "isomorphic". Two graphs that have the same structure are called isomorphic, and we'll define exactly what that means with examples in today's video graph theory lesson! Check out the full Graph Theor
From playlist Graph Theory
Graph Theory: 10. Isomorphic and Non-Isomorphic Graphs
Here I provide two examples of determining when two graphs are isomorphic. If they are isomorphic, I give an isomorphism; if they are not, I describe a property that I show occurs in only one of the two graphs. Here is a related video in which I show how to check for whether these examp
From playlist Graph Theory part-2
Discrete Math II - 10.3.2 Graph Isomorphisms
Let's take a look at whether two graphs are isomorphic. For graphs to be isomorphic they must have the same number of vertices and edges. But more than that, they must also have the same structure. That is, the degree of vertices must match up, as well as the incidence of edges. Video Ch
From playlist Discrete Math II/Combinatorics (entire course)
Lecture 7: From Equivariance to Naturality - Pim de Haan
Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slides: https://www.sci.unich.it/geodeep2022/slides/2022-07-27%20Naturality%20@%20First%20Italian%20GDL%20Summer%20School.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Isomorphic Graphs Have the Same Degree Sequence | Graph Theory
We prove that isomorphic graphs have the same degree sequence. This isn't too surprising since graph isomorphisms preserve adjacency and non-adjacency of vertices by definition. We'll prove it by taking an arbitrary vertex from our graph G, and show it has the same degree as its image unde
From playlist Graph Theory
Global symmetry from local information: The Graph Isomorphism Problem – László Babai – ICM2018
Combinatorics | Mathematical Aspects of Computer Science Invited Lecture 13.4 | 14.5 Global symmetry from local information: The Graph Isomorphism Problem László Babai Abstract: Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity stat
From playlist Combinatorics
Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
25. Interactive Proof Systems, IP
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Introduced the interactive proof syste
From playlist MIT 18.404J Theory of Computation, Fall 2020