7. Suppose a graph G = (V, E) has n vertices and m edges (i.e., |V| = n and |E| = m). Further suppose that m < n and every v E V has degree at least 1. (IHint for both parts below: Handshake lemma.) (a) Prove that 2m > n. Prove that there are at least 2(n – m) vertices which (b) have degree exactly 1. |

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