A tree has 12 vertices. How many edges?

💡 For a tree: n − 1.

Sum of degrees in a graph with 7 edges:

💡 Handshake lemma: Σ deg = 2|E|.

Does a graph with vertex degrees {3, 3, 3, 3, 3} exist?

💡 Sum of degrees must be even (handshake lemma).