Use the Handshaking Lemma to prove that if G is a connected graph with n vertices (where n ≥ 2) and exactly n - 1 edges, then G has at least two vertices of degree 1. (Hint: show that if G was connected but did not have two vertices of degree 1, then G could not have exactly n - 1 edges, which is a contradiction; conclude, therefore, that the at least two vertices of degree 1 must exist.)