In mathematical graph theory, the rooted product of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and for every vertex of G, identify with the root node of the i-th copy of H. More formally, assuming that V(G) = {g1, ..., gn}, V(H) = {h1, ..., hm} and that the root node of H is , define where and If G is also rooted at g1, one can view the product itself as rooted, at (g1, h1). The rooted product is a subgraph of the cartesian product of the same two graphs. (Wikipedia).
This video introduces rooted trees and how to define the relationships among vertices in a rooted tree. mathispower4u.com
From playlist Graph Theory (Discrete Math)
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Given a Rooted Tree, Determine Relationships
This video analyzes the relationships of vertices in a rooted tree. mathispower4u.com
From playlist Graph Theory (Discrete Math)
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
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
Breakdown of the basic components of graphs in graph theory
From playlist Graph Theory
Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions
What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree
From playlist Graph Theory
Underlying Graphs of Digraphs | Directed Graphs, Graph Theory
What are underlying graphs of directed graphs in graph theory? This is a sort of undirected graph that "underlies" or "lies under" a directed graph. But how is it actually defined? We'll go over that in today's video graph theory lesson! A simple way to define the underlying graph of a di
From playlist Graph Theory
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
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogu
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Benjamin Smith, Isogenies in genus 2 for cryptographic applications
VaNTAGe seminar, October 4, 2022 License: CC-BY-NC-SA
From playlist New developments in isogeny-based cryptography
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
Algebra 1 Regents August 2015 #4
A common core sample question on the algebra 1 regents. The full playlist can be found here: https://www.youtube.com/playlist?list=PLntYGYK-wJE0Es8CnihcNsFQKDC8KptIQ
From playlist Algebra 1 Regents August 2015
Cram For Your Test On Radicals
In this video I will try to cover multiple topics regarding simplifying, solving and graphing radicals so that you can ace your next test ⭐️ Cram For Your Exponential and Logarithmic Function Test - https://youtu.be/hoZ_HBs4Xho ✅Study Guides and Reviews - https://youtube.com/playlist?li
From playlist Radicals in Algebra 2
Graphs, vectors and integers - Noga Alon
Noga Alon Tel Aviv University; Visiting Professor, School of Mathematics December 1, 2014 The study of Cayley graphs of finite groups is related to the investigation of pseudo-random graphs and to problems in Combinatorial Number Theory, Geometry and Information Theory. I will discuss thi
From playlist Mathematics
Linear Algebra for Beginners | Linear algebra for machine learning
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. In this course you will learn most of the basics of linear algebra wh
From playlist Linear Algebra
This course is about calculus 3 and the following topics have been presented in this course in very details. ⭐ Table of Contents ⭐ ⌨️ (0:05) Sequences ⌨️ (38:21) Infinite series ⌨️ (1:07:31) The divergence and integral test ⌨️ (1:24:07) Comparison test ⌨️ (1:48:00)
From playlist Calculus
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph Theory
Solve Trigonometric Equations | Analytic Trig | Pre-Calculus
In this video we will explore how to solve trigonometric equations. We will work on isolating the trigonometric function using inverse operations, factoring and identities. We will then solve on the unit circle, all solutions and multiple angles. I make short, to-the-point online math t
From playlist Pc - In the classroom