**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 (*S*_{2}, S_{6}, S_{3}, S_{5}, S_{1}, S_{4}). **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 ...