Graph connectivity | Graph theory objects

Path (graph theory)

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipath) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). Korte et al. (1990) cover more advanced algorithmic topics concerning paths in graphs. (Wikipedia).

Path (graph theory)
Video thumbnail

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

Video thumbnail

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

Video thumbnail

Walks trails paths and cycles

In this tutorial I explore the concepts of walks, trails, paths, cycles, and the connected graph.

From playlist Introducing graph theory

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

The Definition of a Graph (Graph Theory)

The Definition of a Graph (Graph Theory) mathispower4u.com

From playlist Graph Theory (Discrete Math)

Video thumbnail

Introduction to Graph Theory

This lesson introduces graph theory and defines the basic vocabulary used in graph theory. Site: http://mathispower4u.com

From playlist Graph Theory

Video thumbnail

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

Video thumbnail

Introduction to Graph Theory: A Computer Science Perspective

In this video, I introduce the field of graph theory. We first answer the important question of why someone should even care about studying graph theory through an application perspective. Afterwards, we introduce definitions and essential terminology in graph theory, followed by a discuss

From playlist Graph Theory

Video thumbnail

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

Video thumbnail

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

Video thumbnail

The Chinese Postman Problem (Introduction to Graph Theory)

This video covers Eulerian, Semi-Eulerian, and regular graphs in the Chinese Postman Problem as well as applications of graph theory. This was made for 3Blue1Brown's Summer of Math Exploration video competition (link: https://www.3blue1brown.com/blog/some1). For more information about Eu

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

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

Video thumbnail

Diameter and Radius of Tree Graphs | Graph Theory

We discuss what family of tree graphs have maximum diameter, minimum diameter, maximum radius, and minimum radius. Recall the diameter of a graph is the maximum distance between any two vertices. The radius of a graph is the minimum eccentricity of any vertex. We'll find the star graphs ha

From playlist Graph Theory

Video thumbnail

Math Explorations Ep20, Graph theory intro (Mar 11, 2022)

This is a recording of a live class for Math 1015, Mathematics: An Exploration, an undergraduate course for non-technical majors at Fairfield University, Spring 2022. The major topics are voting, gerrymandering, and graph theory. Handouts and homework are at the class website. Class web

From playlist Math 1015 (Mathematical Explorations) Spring 2022

Video thumbnail

What Every Physicist Should Know About String Theory: Edward Witten

https://strings2015.icts.res.in/talkTitles.php Table of Contents (powered by https://videoken.com) 0:00:00 Introduction 0:01:05 [Talk: What Every Physicist Should Know About String Theory by Edward Witten] 0:02:46 Anyone who has studied physics is familiar with the fact that while physics

From playlist Strings 2015 conference

Related pages

Graph (discrete mathematics) | Connectivity (graph theory) | Glossary of graph theory | Hamiltonian path | Floyd–Warshall algorithm | Longest path problem | Polygonal chain | Shortest-path graph | Sequence | End (graph theory) | Path graph | Bellman–Ford algorithm | Graph theory | Self-avoiding walk | Vertex (graph theory) | Dijkstra's algorithm | Distance (graph theory) | Induced path | Directed graph | Shortest path problem | Algorithm