In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree. (Wikipedia).
What is a Graph Cycle? | Graph Theory, Cycles, Cyclic Graphs, Simple Cycles
What is a graph cycle? In graph theory, a cycle is a way of moving through a graph. We can think of a cycle as being a sequence of vertices in a graph, such that consecutive vertices are adjacent, and all vertices are distinct except for the first and last vertex, which are required to be
From playlist Graph Theory
What are Cycle Graphs? | Graph Theory, Graph Cycles, Cyclic Graphs
What are cycle graphs? We have talked before about graph cycles, which refers to a way of moving through a graph, but a cycle graph is slightly different. A cycle graph is what you would get if you took the vertices and edges of a graph cycle. We can think of cycle graphs as being path gra
From playlist Graph Theory
In this tutorial I explore the concepts of walks, trails, paths, cycles, and the connected graph.
From playlist Introducing graph theory
Graph Theory Talk: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues
Graph Theory Stuff: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues
From playlist Graph Theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
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
What is a Path? | Graph Theory
What is a path in the context of graph theory? We go over that in today's math lesson! We have discussed walks, trails, and even circuits, now it is about time we get to paths! Recall that a walk is a sequence of vertices in a graph, such that consecutive vertices are adjacent. A path is t
From playlist Graph Theory
What is a Path Graph? | Graph Theory
What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can
From playlist Graph Theory
Graph Theory: 02. Definition of a Graph
In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio
From playlist Graph Theory part-1
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
Extremal theory of ordered graphs – Gábor Tardos – ICM2018
Combinatorics Invited Lecture 13.3 Extremal theory of ordered graphs Gábor Tardos Abstract: We call simple graphs with a linear order on the vertices ‘ordered graphs’. Turán-type extremal graph theory naturally extends to ordered graphs. This is a survey on the ongoing research in the ex
From playlist Combinatorics
Hamiltonian Cycles, Graphs, and Paths | Hamilton Cycles, Graph Theory
What are Hamiltonian cycles, graphs, and paths? Also sometimes called Hamilton cycles, Hamilton graphs, and Hamilton paths, we’ll be going over all of these topics in today’s video graph theory lesson! A Hamilton cycle in a graph G is a cycle containing all vertices of G. A Hamilton path
From playlist Graph Theory
Overview of algorithms in Graph Theory
An overview of the computer science algorithms in Graph Theory Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-theory-algorithms Previous video (intro): h
From playlist Graph Theory Playlist
Graph Theory: 38. Three ways to Identify Trees
A proof that a graph of order n is a tree if and only if it is connected and has n-1 edges. This, together with the previous video and the definition of a tree, gives three ways to determine if a graph is a tree. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http:/
From playlist Graph Theory part-7
Graph Theory: 33. Petersen Graph is Not Hamiltonian
An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/FgHuQw7kb-o - Graph Theory: 30. The 5 Known Vertex-Transitive Non-Hamiltonian Graphs http://youtu.be/XA8MDEYNWx8 - Graph Theory: 31. Lemma on Hamiltonian Graphs http://youtu.be/0ksOKghZKdo - Graph Theo
From playlist Graph Theory part-6
Lecture 20 - Trees and Connectivity
This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Proof: Closed Odd Walk contains Odd Cycle | Graph Theory
We prove that a closed odd walk contains an odd cycle. This result is also part of the proof that a graph is bipartite if and only if it contains no odd cycles, so it's important! The argument has to do with the fact that an odd closed walk can be broken down into cycles, and one of these
From playlist Graph Theory
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
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics