# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.08

## Topology

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## 4. TRAVERSABLE NETWORKS

### EXERCISE C

- 1. (a) Show that networks in figure 27 are traversable and add three more traversable networks. (b) Mark the point where you start (S) and the point where you finish(F).
- 2. Draw four traversable networks of your own, showing the start and finish.
- 3. Draw a traversable network with two 2nodes and no other nodes. Where can you start and finish? Can you start from more than one point? Can you draw a network with just two 2nodes which is not traversable?
- (figure available in print form)
- 4. Which of the networks in figure 26 are traversable? You may have to try several starting points before you either succeed or decide that the network is not traversable. NOTE: Provide each student a copy of figure 26 and the following table.

Net- | Total Number | Number of | Number of | Is Network |

work | of Nodes | Even-Nodes | Odd-Nodes | Traversable? |

1. | 2 | 2 | — | Yes |

2. | 4 | — | 4 |

.

10.

Note: In figure 26 network 1: A is an even node because 4 arcs meet at A and B is also an even node. In network 2: A, B, C, and D are odd nodes because 3 arcs meet at each node.

### INVESTIGATION 3

Investigate possible starting and finishing points in traversable networks. When is a network traversable?SUGGESTION: Note odd and even nodes. Look carefully at answers to question 4.

### INVESTIGATION 4

The drawings in figure 28 are not traversable.

- a) What is the least number of strokes in which each can be drawn?
- b) Can you find a rule for deciding how many strokes you need by just looking at a figure?
- c) How many extra lines we must add in order to make each drawing in figure 28 traversable and add 5 more non traversable networks to the list.