Most problems for this homework are from the textbook. Please note that I have changed the content of some of them.

**1.** 10 (page 56). (10 points) Also answer the following questions:

- a) is the graph connected or not? (3 points)
- b) is there any cycle in the graph? If you answerr is yes, then show one cycle. (4 points)
- c) is the graph complete? (3 points)

There is a total of 20 points for this problem.

**2.** 14 (page 56) (2*10 = 20 points)

**3.** Assume that the digraph in figure 1.28 (page 56) represents a relation R over the set A={a, b, c, d, e, f}.

- a) show the set representation of R (5 points)
- b) show the matrix representation of R (5 points)
- c) is R reflexive? (3 points)
- d) is R irreflexive (3 points)
- e) is R symmetric (3 points)
- f) is R asymmetric? (3 points)
- g) is R antisymmetric? (3 points)
- h) is there any sink in the digraph? (2 points)
- i) is there any source in the digraph? (2 points)
- j) write down all paths of length two starting from d (6 points)

**4.** 16 (page 56) (10 points)

**5.** 4 (page 96) (14*5 = 70 points)

**6.** 7 (page 97) with the difference that *h(four) = 0* instead of 8 as indicated in the problem. (7+7+6 = 20 points)

Maximum mark: 175 (100%)