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.
Recall that the size of a graph is the number of edges it has. The degree of a vertex is the number of edges incident to the vertex. So the theorem tells us that if a graph has m edges, then the sum of the degrees of all vertices in the graph is twice m, or 2m. If you think about this for a minute, it should seem pretty intuitive.
Each edge in a graph contributes 1 to the degree count of two different vertices, because each edge is incident to two vertices. So, each edge contributes 2 to the total degree count of all vertices in the graph, so the total degree count is two times the number of edges, or 2m, where m is the size of the graph.
Check out the Halloween Special!:
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow’s music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp:
Vallow Soundcloud:
Vallow SoundCloud:
********************************************************************
WRATH OF MATH
◆ Support Wrath of Math on Patreon:
Follow Wrath of Math on...
● Instagram:
● Facebook:
● Twitter:
Music Channel:
1 view
152
33
1 month ago 00:29:28 1
🎥 Can you guess the Anime by the First 10 Seconds? 🔥 Anime Quiz
1 month ago 00:03:37 1
Админы Актуального Курска и другие куряне, покажите общественные туалеты Курска .?!) #курскиймайор
1 month ago 11:55:00 1
13 minutes ago! First Largest US Naval Base Bombarded by Russian MIG 29 Arma3
1 month ago 00:02:36 1
Five Little Elves | Christmas Song For Kids | Super Simple Songs
1 month ago 00:02:36 5
Jingle Bells | Christmas Song | Super Simple Songs
1 month ago 00:03:02 1
Milk & Cookies | Holiday Song for Kids | Rhymington Square
1 month ago 00:05:32 1
Queen - Bohemian Rhapsody (Live at Rock Montreal, 1981) [HD]
1 month ago 00:27:21 1
When Shoegaze Meets Electronica
1 month ago 00:21:40 1
La Toya Jackson On Michael’s Allegations | What Changed Her Mind? | the detail.
1 month ago 00:06:44 1
First Base - Love Is Paradise (Club Mix)
1 month ago 00:25:19 1
Существа в открытом космосе возможны? / Большой Взрыв наоборот / Астрообзор #169
1 month ago 00:00:37 1
I AM KIRA || Death Note
1 month ago 00:04:14 1
The Hunter - Bloodborne (4K UHD 2024)
1 month ago 00:04:35 1
My Girl OST - Sang-eo-reul Sa-rang-han In-eo (Male Version)
1 month ago 00:00:59 1
Melania Trump is doing things differently this time
1 month ago 00:05:15 1
Aeon Flux - “War“ (New Original Soundtrack and Sound Design)
1 month ago 00:18:51 1
How to Sound Fluent in English FAST!
1 month ago 00:01:20 1
Big wildcat tenderness
1 month ago 00:04:27 1
Botsol vs. Leads Sniper: Email Extractor Showdown 🔥
1 month ago 00:13:57 1
Why did Davy Jones Look SO Realistic?
1 month ago 00:09:46 1
Денис Фёдоров, Большая фуга на тему «В траве сидел кузнечик» и множество других тем.
1 month ago 01:10:29 1
Поиграли в 8 пропущенных игр [РефАААнд?!]
1 month ago 00:06:11 1
масло и жирная баба.mov
1 month ago 01:04:51 18
Half in the Bag: Top 10 Horror Movies (2024) Part 2