Students will learn what it means for vertices to adjacent, as seen here. They'll also learn how to determine the degree of a vertex, as seen here. Then they'll learn what the *Handshaking lemma* says and how to prove it. Further, students will learn how the *Handshaking lemma* can be used to prove that every graph has an even number of odd degree vertices. Here's a video on the *Handshaking lemma* and its corollary.