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. (b) have degree exactly 1. Prove that there are at least 2(n – m) vertices which

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

Extracted text: 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="" €="" v="" has="" degree="" at="" least="" 1.="" (ihint="" for="" both="" parts="" below:="" handshake="" lemma.)="" (a)="" prove="" that="" 2m=""> n. (b) have degree exactly 1. Prove that there are at least 2(n – m) vertices which

Jun 04, 2022

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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. (b) have degree exactly 1. Prove that there are at least 2(n – m) vertices which

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