In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex is denoted or . The maximum degree of a graph , denoted by , and the minimum degree of a graph, denoted by , are the maximum and minimum of its vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0. In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph (denoted , where is the number of vertices in the graph) is a special kind of regular graph where all vertices have the maximum possible degree, . In a signed graph, the number of positive edges connected to the vertex is called positive deg and the number of connected negative edges is entitled negative deg. (Wikipedia).
The degrees of a graph are the number of edges incident upon it. Note that a loop counts as two edges. In a regular graph, all the nodes have a similar degree. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale
From playlist Introducing graph theory
A walkthrough of the degree and valence value of vertices in graph theory
From playlist Graph Theory
Degree Sequence of a Graph | Graph Theory, Graphical Sequences
What is a degree sequence of a graph? Are graphs with the same degree sequence isomorphic? Do isomorphic graphs have the same degree sequence? We’ll go over all of this in today’s video graph theory lesson! Recall that the degree of a vertex is the number of edges incident to the vertex.
From playlist Graph Theory
Graph Theory: 44. Degree Sequence of a Tree
In this video I provide a proof of a necessary and sufficient condition for a sequence of positive integers to be a degree sequence of a tree. Bits of Graph Theory by Dr. Sarada Herke. Links to the related videos: http://youtu.be/aNKO4ttWmcU - Graph Theory: 42. Degree Sequences and Graph
From playlist Graph Theory part-8
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
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Bound on the Sum of Minimum Degrees of Graphs and their Complements | Graph Theory Proofs
We know the degree of a vertex in a simple graph with n vertices has an upper bound of n-1. The degree of a vertex is n-1 when it is adjacent to every vertex in the graph except for itself (it cannot be adjacent to itself). Then certainly the minimum degree of a graph is less than or equal
From playlist Graph Theory
Algorithms Course - Graph Theory Tutorial from a Google Engineer
This full course provides a complete introduction to Graph Theory algorithms in computer science. Knowledge of how to create and design excellent algorithms is an essential skill required in becoming a great programmer. You will learn how many important algorithms work. The algorithms are
From playlist Computer Science Concepts
Graph Theory: 45. Specific Degrees in a Tree
In this video I explain a Theorem which gives an equation involving the number of vertices of specific degrees in any non-trivial tree (a tree with at least 2 vertices). I show how the result works with an example and then explain the proof. -- Bits of Graph Theory by Dr. Sarada Herke.
From playlist Graph Theory part-8
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
Proof: Every Graph has an Even Number of Odd Degree Vertices | Graph Theory
How do we prove that every graph has an even number of odd degree vertices? It seems like a surprising result, how could it be that every graph has such a neat little property? In this video graph theory lesson, we'll prove that every graph has an even number of odd degree vertices, to und
From playlist Graph Theory
Lecture 19 - Degree Sequences & Invariants
This is Lecture 19 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%2019.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
The First Theorem of Graph Theory | Graph Theory
What is The First Theorem of Graph Theory? This theorem gets its name from the fact that it is often the first theorem encountered when one is learning graph theory. The first theorem tells us that if a graph G has size m, then the sum of the degrees of all vertices of G is equal to 2m.
From playlist Graph Theory
Graph Theory: 47. Subgraphs of Regular Graphs
Here I describe a construction technique used by Konig to prove that for every graph G of maximum degree r there exists an r-regular graph which contains G as an induced subgraph. I show how to use the construction with an example and discuss a related question. -- Bits of Graph Theory by
From playlist Graph Theory part-8
Graph Theory: 01. Seven Bridges of Konigsberg
The Seven Bridges of Konigsberg Problem was solved by Euler in 1735 and that was the beginning of Graph Theory! In this video, we explain the problem and the method that Euler used to solve it. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An intro
From playlist Graph Theory part-1
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
8ECM Abel Lecture: László Lovász
From playlist 𝙋𝙧𝙞𝙯𝙚 𝙇𝙚𝙘𝙩𝙪𝙧𝙚𝙨
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
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
Graph Theory: 06 Sum of Degrees is ALWAYS Twice the Number of Edges
This is usually the first Theorem that you will learn in Graph Theory. We explain the idea with an example and then give a proof that the sum of the degrees in a graph is twice the number of edges. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https
From playlist Graph Theory part-1