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 understand just why it's true!

For this proof, we'll need to know the first theorem of graph theory, which states that the sum of all vertex degrees in a graph is equal to twice the number of edges. This is because each edge in a graph is incident to exactly two vertices, and thus each edge contributes 2 to the total degree count of the graph. Check out my lesson on the first theorem of graph theory for more explanation:    • The First Theorem of Graph Theory | G...  

If you're taking a course in Graph Theory, or preparing to, you may be interested in the textbook that introduced me to Graph Theory: “A First Course in Graph Theory“ by Gary Chartrand and Ping Zhang. It’s a wonderful text! You can purchase this book through my Amazon affiliate link below! Using the affiliate link costs you nothing extra, and helps me continue to work on Wrath of Math!

PURCHASE "A First Course in Graph Theory": https://amzn.to/31hgvvJ



I hope you find this video helpful, and be sure to ask any questions down in the comments!

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