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. 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: