# Graph (discrete mathematics)

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A. In contrast, if an edge from a person A to a person B means that A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated. Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by J. J. Sylvester in 1878 due to a direct relation between mathematics and chemical structure (what he called a chemico-graphical image). (Wikipedia).

Discrete Math - 10.1.1 Introduction to Graphs

A brief introduction to graphs including some terminology and discussion of types of graphs and their properties. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

The Definition of a Graph (Graph Theory)

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

From playlist Graph Theory (Discrete Math)

More Graph Theory Definitions

This video explains the definitions of simple graphs, multigraphs, connected and not connected graphs, complete graphs, and the Handshake lemma. mathispower4u.com

From playlist Graph Theory (Discrete Math)

INTRODUCTION to GRAPH THEORY - DISCRETE MATHEMATICS

We introduce a bunch of terms in graph theory like edge, vertex, trail, walk, and path. #DiscreteMath #Mathematics #GraphTheory Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Math

From playlist Discrete Math 2

Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o

From playlist Graph Theory FAQs

Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

Graph theory full course for Beginners

In mathematics, graph #theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A #graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction i

From playlist Graph Theory

[Discrete Mathematics] Planar Graphs

We look at planar graphs and how to determine if a graph is planar or not. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Discrete Mathem

From playlist Discrete Math 2

Degree of Vertices | Definition, Theorem & Example | Graph Theory

The degree of a vertex in Graph Theory is a simple notion with powerful consequences. Simply by counting the number of edges that leave from any vertex - the degree- we get theorems that make it impossible for a group of, say, 5 people to each shake the hands of exactly 3 people at a party

The Abel Prize announcement 2021 - Avi Wigderson and László Lovász

0:49 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 1:38 Citation by Hans Munthe-Kaas, Chair of the Abel committee 10:22 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 17:43

From playlist The Abel Prize announcements

[Discrete Mathematics] Graph Coloring and Chromatic Polynomials

From playlist Discrete Math 2

Gauß Lecture in Leipzig 2022 | László Lovász - Discrete or Continuous

László Lovász, professor at Eötvös Loránd University and Alfréd Rényi Institute of Mathematics in Budapest, gave the distinguished Gauß lecture on the topic Discrete or Continuous?, the question of the continuous nature of our world from a mathematical perspective. This ceremonial event of

From playlist Various Lectures

[Discrete Mathematics] Hamilton Cycles

We introduce the concept of Hamilton Cycles in Graph Theory. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Discrete Mathematics 2: https

From playlist Discrete Math 2

Epic Math Book Speed Run

In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t

From playlist Book Reviews

Discrete Math Book for Beginners

This is a really good discrete math book for beginners. I think this is easier to read than some of the other discrete math books out there. If you are taking discrete math I highly recommend this one. The book is called Discrete Mathematical Structures and it was written by Kolman, Busby

From playlist Book Reviews

ISOMORPHISMS and BIPARTITE GRAPHS - DISCRETE MATHEMATICS

In this video we look at isomorphisms of graphs and bipartite graphs. We also look at complete bipartite graphs and their complements. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/play

From playlist Discrete Math 2

Abel Prize award ceremony 2021

The ceremony honours both the 2020-winners, Hillel Furstenberg and Gregory Margulis, and the 2021-winners, Avi Wigderson and László́ Lovász. 0:30 Haddy N'jie sings Feeling Good 3:18 Welcome by Master of ceremonies, Haddy N'jie 4:46 On the nomination process and the work of the Abel Prize

From playlist Gregory Margulis

[Discrete Mathematics] Subgraphs, Complements, and Complete Graphs

In this video we look at subgraphs, spanning subgraphs, complements, complete graphs, and some relevant theorems. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6

From playlist Discrete Math 2

Discrete Math - 10.2.2 Special Types of Graphs

Introduction to cycles, wheels, complete graphs, hypercubes and bipartite graphs, including using the graph coloring technique to determine if a graph is bipartite. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII

From playlist Discrete Math I (Entire Course)