EXERCISE C
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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).
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2. Draw four traversable networks of your own, showing the start and finish.
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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?
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(figure available in print form)
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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.
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Net-
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Total Number
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Number of
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Number of
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Is Network
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|
work
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of Nodes
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Even-Nodes
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Odd-Nodes
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Traversable?
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1.
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2
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2
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—
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Yes
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2.
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4
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—
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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.
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a) What is the least number of strokes in which each can be drawn?
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b) Can you find a rule for deciding how many strokes you need by just looking at a figure?
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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.
