At the start of the solution, I understand that any tree with four vertices has three edges. I don't understand the next statement: "Thus the total degree of a tree with four vertices must be 6." This seems trivial but my brain is a bit tired. How does this follow? Vertices in trees can have degree greater than 2, right?
Best Answer
Each edge contributes to the degrees of two vertices. Thus, the total degree is twice the number of edges.