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### Chapter 10

#### Section 10.1

1. a. (1,2, 1). b. (1, 3, 5, 1,2). c. (1, 2, 3, 4, 5, 3, 1).

3. a. (1, 2, 3, 4, 5, 1, 3, 5). b. (1, 2, 3, 4, 5, 3, 1). c. (1, 2, 3, 4, 5, 1).

5. a. 6. c. 10.

6. a. 4. c. 10.

7. a. 4. c. 5.

8. a. Yes. c. No. e. No.

9. a. Yes. c. No.

10. 90 edges.

12. 153 edges.

13. Let the vertices of G be the numbers in the set {1, 2, 3, 4} and let G have three edges that make up the path (1, 2, 3, 4). Then the complement of G has three edges that make up the path (2, 4, 1, 3).

15. a. Yes. c. No.

16. a. The complement is the path (S2, S6, S3, S5, S1, S4). b. An edge in the complement means that the two committees have no members in common and can meet at the same time.

17. a. 2 hours. c. 5 hours.

18. a. A “star” with an extra edge between ...

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