# Mth/221 Discrete Math for Information Technology Week 4

### Mth/221 Discrete Math for Information Technology Week 4

* MTH/221 Week Four Individual problems:*

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Ch. 11 of Discrete and Combinatorial Mathematics

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Exercise 11.1, problems 8, 11 , text-pg:519

Exercise 11.2, problems 1, 6, text-pg:528

Exercise 11.3, problems 5, 20 , text-pg:537

Exercise 11.4, problems 14 , text-pg:553

Exercise 11.5, problems 7 , text-pg:563

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Ch. 12 of Discrete and Combinatorial Mathematics

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Exercise 12.1, problems 11 , text-pg:585

Exercise 12.2, problems 6 , text-pg:604

Exercise 12.3, problems 2 , text-pg:609

Exercise 12.5, problems 3 , text-pg:621

Chapter 11

Exercise 11.1

Problem 8:

Figure 11.10 shows an undirected graph representing a section

of a department store. The vertices indicate where cashiers

are located; the edges denote unblocked aisles between cashiers.

The department store wants to set up a security system where

(plainclothes) guards are placed at certain cashier locations so

that each cashier either has a guard at his or her location or is

only one aisle away from a cashier who has a guard. What is

the smallest number of guards needed?

Figure 11.10

Problem 11:

Let G be a graph that satisfies the condition in Exercise 10.

(a) Must G be loop-free? (b) Could G be a multigraph? (c) If

G has n vertices, can we determine how many edges it has?

Exercise 11.2

Problem 1:

Let G be the undirected graph in Fig. 11.27(a).

a) How many connected subgraphs ofGhave four vertices

and include a cycle?

b) Describe the subgraph G1 (of G) in part (b) of the figure

first, as an induced subgraph and second, in terms of

deleting a vertex of G.

c) Describe the subgraphG2 (ofG) in part (c) of the figure

first, as an induced subgraph and second, in terms of the

deletion of vertices of G.

d) Draw the subgraph of G induced by the set of vertices

U _ {b, c, d, f, i, j}.

e) For the graph G, let the edge e _ {c, f }. Draw the subgraph

G − e.

Figure 11.27

Problem 6:

Find all (loop-free)...