Page 20 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4 Mathematics Chapter 5 Network in Graph Theory

Represent information in the form of Solution:
networks Langkawi Kota Kinabalu
Kota Bharu
Example 18 Pulau Sibu Tawau
Pinang Kuching
The diagram below shows some roads in an area.
Kuala
Lumpur Johor Bahru

Try question 19 in Formative Zone 5.1
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Example 20
Five friends Asiah, Khairul, Natifah, Roslan and
Zeti made conversation by video calls in the
By using the road junction as vertex and the road following situation.
CHAP. as edge, draw an undirected graph to represent
5 the network of the roads. Asiah called Khairul and Roslan but not Natifah
Solution: or Zeti. Zeti only called Roslan and Natifah. Zeti
had never called Khairul although Khairul always
called Zeti. Often Natifah and Roslan will call
one another as Khairul and Natifah.
Draw a directed graph to represent the
conversation by video calls described in the
situation.
Solution:
Natifah
Try question 18 in Formative Zone 5.1
Khairul

Example 19 Zeti

The diagram below shows some locations of Roslan Asiah
airports in Malaysia.
Try question 20 in Formative Zone 5.1
Langkawi Kota Kinabalu
Kota Bharu
Sibu Solve problems involving networks
Pulau Tawau
Pinang Kuching
Example 21
Kuala
Lumpur Johor Bahru The diagram below shows a network of roads
connecting five places A, B, C, D and E.
A company Air X scheduled 10 flights on a day
as follows. 200 D

• Pulau Pinang to Johor Bahru B 340 C 100 270
• Kuching to Tawau 400 120
• Tawau to Kuching
• Kuching to Kuala Lumpur A 350 E
• Kota Kinabalu to Kuala Lumpur
• Kuala Lumpur to Langkawi The weights stated on each edge represent the
• Langkawi to Pulau Pinang distances, in m, between two places. A path is
• Johor Bahru to Sibu a route along the edges of the graph from one
• Pulau Pinang to Kota Bharu vertex to the other vertices without repeating any
• Kuala Lumpur to Kuching one vertex.
By listing down all the possible paths, determine
Draw a directed graph to represent the information the shortest path from A to C and state its length.
of the flights.

100 5.1.4 5.1.5

ENG05 Spotlight Matematik F4.indd 100 14/01/2021 9:56 PM