Parametric families of graphs | Trees (graph theory)
In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are {vi, vi+1} where i = 1, 2, …, n − 1. Equivalently, a path with at least two vertices is connected and has two terminal vertices (vertices that have degree 1), while all others (if any) have degree 2. Paths are often important in their role as subgraphs of other graphs, in which case they are called paths in that graph. A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See, for example, Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). (Wikipedia).
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
Section 4b: Graph Connectivity
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
In this tutorial I explore the concepts of walks, trails, paths, cycles, and the connected graph.
From playlist Introducing graph theory
Graph Theory: 16. Walks Trails and Paths
Here I explain the difference between walks, trails and paths in graph theory. --An introduction to Graph Theory by Dr. Sarada Herke. Problem Set #3: https://docs.google.com/file/d/0ByUyHC8zuQ1sOWpici14V3cxOGM/edit?usp=sharing For quick videos about Math tips and useful facts, check out
From playlist Graph Theory part-3
What is a Walk? | Graph Theory
What is a walk in the context of graph theory? That is the subject of today's math lesson! A walk in a graph G can be thought of as a way of moving through G, where you start at any vertex in the graph, and then move to other vertices through the edges in the graph. In a walk, you are allo
From playlist Graph Theory
Find the Shortest Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Graph Data Structure 6. The A* Pathfinding Algorithm
This is the sixth in a series of videos about the graph data structure. It includes a step by step walkthrough of the A* pathfinding algorithm (pronounced A Star) for a weighted, undirected graph. The A* pathfinding algorithm, and its numerous variations, is widely used in applications suc
From playlist Path Finding Algorithms
Introduction to Euler Paths and Euler Circuits
This video introduces Euler paths and Euler circuits. mathispower4u.com
From playlist Graph Theory (Discrete Math)
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture focuses on solving any all-pairs shortest paths (APSP) in w
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture introduces a single source shortest path algorithm that wor
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This session focuses on preparing for the quiz. High-level concepts are
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
Proof: Menger's Theorem | Graph Theory, Connectivity
We prove Menger's theorem stating that for two nonadjacent vertices u and v, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths. If you want to learn about the theorem, see how it relates to vertex connectivity, and see
From playlist Graph Theory
Proof: Necessary Component Condition for Graphs with Hamiltonian Paths | Graph Theory
Let G be a graph with a Hamiltonian path (a path containing all vertices of the graph). Then, if we delete any k vertices of G, the resulting graph will have at most k+1 components. We prove this result in today's video graph theory lesson! This is a fairly straightforward proof by induct
From playlist Graph Theory
Existence of Eulerian Paths and Circuits | Graph Theory
Explanation video on how to verify the existence of Eulerian Paths and Eulerian Circuits (also called Eulerian Trails/Tours/Cycles) Euler path/circuit algorithm: https://youtu.be/8MpoO2zA2l4 Euler path/circuit source code: https://youtu.be/QQ3jO1dKjYQ Algorithms repository: https://githu
From playlist Graph Theory Playlist
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture discusses weighted graphs and weighted paths. This prepares
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
What is a Circuit? | Graph Theory
What is a circuit in graph theory? That is the subject of today's math lesson! Remember that a trail is a sequence of vertices in a graph such that consecutive vertices are adjacent in that graph, and no edge is traversed more than once, which means if the vertex b follows a in some part o
From playlist Graph Theory
What is the limit of a sequence of graphs?? | Benjamini-Schramm Convergence
This is an introduction to the mathematical concept of Benjamini-Schramm convergence, which is a type of graph limit theory which works well for sparse graphs. We hope that most of it is understandable by a wide audience with some mathematical background (including some prior exposure to g
From playlist Summer of Math Exposition Youtube Videos