In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: * the vertex set of G □ H is the Cartesian product V(G) × V(H); and * two vertices (u,u' ) and (v,v' ) are adjacent in G □ H if and only if either * u = v and u' is adjacent to v' in H, or * u' = v' and u is adjacent to v in G. The Cartesian product of graphs is sometimes called the box product of graphs [Harary 1969]. The operation is associative, as the graphs (F □ G) □ H and F □ (G □ H) are naturally isomorphic.The operation is commutative as an operation on isomorphism classes of graphs, and more strongly the graphs G □ H and H □ G are naturally isomorphic, but it is not commutative as an operation on labeled graphs. The notation G × H has often been used for Cartesian products of graphs, but is now more commonly used for another construction known as the tensor product of graphs. The square symbol is intended to be an intuitive and unambiguous notation for the Cartesian product, since it shows visually the four edges resulting from the Cartesian product of two edges. (Wikipedia).
Graph Theory: 49. Cartesian Product of Graphs
What is the Cartesian product of two graphs? We start with a reminder of what this means just for sets and then provide the formal definition for graphs. We include a few examples to become familiar with the idea and we also briefly discuss what a hypercube (or n-cube) is in graph theory
From playlist Graph Theory part-8
What is the Cartesian Product of Sets? | Set Theory
What is the Cartesian product of two sets? The Cartesian product can be generalized to more than two sets, but in this video we go over Cartesian products of two sets! Here is how it works. If you have two sets, A and B, then their Cartesian product, written A x B, is the set containing al
From playlist Set Theory
The Basics of Sets | Cartesian Products
We define the Cartesian product of sets and work through several examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Research Gate profile:
From playlist Proof Writing
The Cartesian Product of Two Sets
This video explains how to find the Cartesian product of two sets.
From playlist Sets (Discrete Math)
Cartesian Product of Two Sets A x B
Learning Objectives: 1) Define an ordered pair 2) Define the Cartesian Product of two sets 3) Find all the elements in a Cartesian Product **************************************************** YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask q
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
CARTESIAN PRODUCTS and ORDERED PAIRS - DISCRETE MATHEMATICS
We introduce ordered pairs and cartesian products. We also look at the definition of n-tuples and the cardinatliy of cartesian products. LIKE AND SHARE THE VIDEO IF IT HELPED! Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http
From playlist Discrete Math 1
Cartesian Products with Empty Sets | Set Theory, Cartesian Product of Sets, Empty Set
How do Cartesian products work with empty sets? Cartesian products are great and all, but we cannot eagerly dive into working with them without making sure we know how to deal with Cartesian products when empty sets are involved. We go over that in today's math lesson! Recall that the Car
From playlist Set Theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Topology 1.4 : Product Topology Introduction
In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Induction, bijections, products -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Video 7: Introduction to Functions
MIT HFH.101 Indian Institutes of Technology Joint Entrance Exam Preparation, Fall 2016 View the complete course: https://ocw.mit.edu/high-school/iit-jee/exam-prep Instructor: Vaibhav Unhelkar In this video, we introduce the topic of functions. We discuss three ways to describe the functio
From playlist MIT Indian Institutes of Technology Joint Entrance Exam Preparation, Fall 2016
Chris Godsil: Problems with continuous quantum walks
Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the proper
From playlist Combinatorics
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
Jezus Gonzalez (6/25/17) Bedlewo: Topological complexity and the motion planning problem in robotics
Early this century Michael Farber introduced the concept of Topological Complexity (TC), a model to study the continuity instabilities in the motion planning problem in robotics. Farber’s model has captured much attention since then due to the rich algebraic topology properties encoded by
From playlist Applied Topology in Będlewo 2017
MAST30026 Lecture 12: Function spaces (Part 2)
The aim of this lecture was to motivate the definition of the compact-open topology on function spaces, via the adjunction property. I explained how any topology making the adjunction property true must include a certain class of open sets, which we will define next lecture to be a sub-bas
From playlist MAST30026 Metric and Hilbert spaces
Lecture 27 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his discussion on higher dimensions and the outer reaches while helping the students understand higher dimensions Fourier Transforms.
From playlist Lecture Collection | The Fourier Transforms and Its Applications
From playlist 3d graphs