🎯 Odd Degree Corollary

Every graph has an even number of vertices with odd degree.

Proof: By the Handshaking Lemma, $\\sum d(v) = 2|E|$ is even. Split the sum into odd-degree and even-degree vertices. The even-degree sum is even, so the odd-degree sum must also be even. Since each odd-degree term is odd, there must be an even number of such terms.

From: Introduction to Graph Theory

Learn more: https://west-graphs-deploy.vercel.app/#/section/3

Explore all courses: https://mathacademy-cyan.vercel.app