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# HW1 - Solution to HW 1 Ning SUN 1.1 4 1.2 4 5(b c k 6(a e...

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Unformatted text preview: Solution to HW 1 Ning SUN July 19, 2009 1.1: 4; 1.2: 4, 5 (b, c, k ), 6 (a, e); 1.3: 4,8; 1.4: 3 (f, j), 7 (f, i), 16; 2.1: 2. 1.1#4 (a) J-John, M-Mary, R-Rose, S-Steve, T-Ted, W-Wendy (b) 2 days. John talks to Mary (or Wendy) on the rst day, and this person talks to Steve on the second day. (c) If John and Mary stopped talking (or John and Wendy), it would take 3 days for a rumor started by John to reach everyone. 1.2#4 No . You can easily show that the left graph is non-planar, while the right one is planar. So they cannot be isomorphic. 1.2#5 You can nd the solutions in your book. 1.2#6 (a) No . Left: 3 vertices of degree 4 Right: 2 vertices of degree 4. (e) No . Left: 4 vertices of degree 4: b, c, e, f * Each of them connects with two vertices of degree 4, and two vertices of degree 3 * (for example, b connects with a, c, e, g, where deg(e)=deg(c)=4, deg(a)=deg(f)=3) Right: 4 vertices of degree 4: 1, 3, 6, 8 1 * Each of them connects with one vertex of degree 4, and three vertices of degree 3...
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