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.