In graph theory, two graphs and are homeomorphic if there is a graph isomorphism from some of to some subdivision of . If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in illustrations), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if they are homeomorphic in the topological sense. (Wikipedia).
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
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
Graph Theory: Isomorphisms and Connectedness
This video is about isomorphisms between graphs and connectedness of graphs.
From playlist Basics: Graph Theory
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
In-Neighborhoods and Out-Neighborhoods in Digraphs | Graph Theory
We discuss neighborhoods in the context of directed graphs. This requires that we split the concept of "neighborhood" in two, since a vertex v could be adjacent TO a vertex u, or adjacent FROM the vertex u. Thus, the outneighborhood of a vertex v is the set of vertices v is adjacent to, an
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: 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
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
What are Geodesics? | Graph Theory
What are geodesics in graph theory? We'll define them and give some examples in today's video graph theory lesson! And apologies for my mispronunciation and misspelling in this video. Remember that the distance between two connected vertices is the length of a shortest path connecting th
From playlist Graph Theory
Sebastian Hensel: Fine curve graphs and surface homeomorphisms
CONFERENCE Recording during the thematic meeting : "Big Mapping Class Group and Diffeomorphism Groups " the October 10, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mat
From playlist Dynamical Systems and Ordinary Differential Equations
Are a line and a square the same shape? | Introduction to Topology #SoME2
Is a line really different than a square? Watch the video to find out! In this video, you will learn exactly what topology is all about through dimension! This video was created for the 2022 Summer of Math Exposition. 00:00 Introduction: Is a Line Equal to a Square? 1:22 The Dimension
From playlist Summer of Math Exposition 2 videos
Danny Calegari: Big Mapping Class Groups - lecture 1
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
Group actions on 1-manifolds: A list of very concrete open questions – Andrés Navas – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.8 Group actions on 1-manifolds: A list of very concrete open questions Andrés Navas Abstract: Over the last four decades, group actions on manifolds have deserved much attention by people coming from different fields
From playlist Dynamical Systems and ODE
Barcodes for Hamiltonian homeomorphisms of surfaces -Benoît Joly
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Barcodes for Hamiltonian homeomorphisms of surfaces Speaker: Benoît Joly Affiliation: Ruhr-Universität Bochum Date: March 25, 2022 In this talk, we will study the Floer Homology barcodes from a dynamical poin
From playlist Mathematics
Emily Stark: The visual boundary of hyperbolic free-by-cyclic groups
Abstract: Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, th
From playlist Topology
Danny Calegari: Big Mapping Class Groups - lecture 4
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
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Karen Vogtmann - Outer space for right-angled Artin groups
Karen Vogtman (Cornell University, USA) Right-angled Artin groups interpolate between free groups and free abelian groups, so one may think of their outer automorphism groups as interpolating between Out(F_n) and GL(n,Z). I will describe an Outer space for these automorphism groups which
From playlist T1-2014 : Random walks and asymptopic geometry of groups.