Page 18 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
Chapter 5 Network in Graph Theory Mathematics 4

Solution:
(a) BRILLIANT Tips
The weight on the edge of a weighted graph may
represents distance, time, cost, price and so on.

Directed graph Example 10
(b) State whether each of the following graphs
represents a weighted graph or an unweighted
graph.
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(a) (b)
3
5
(c) Undirected 10
graph 2
7
(c) 11 CHAP.
2 5

6 5 4
Try question 8 in Formative Zone 5.1 2
3
Example 9 Solution:
A graph has vertices {A, B, C, D} and edges {(A, A), (a) A weighted graph
(A, B), (A, D), (B, C), (C, A), (C, B)}. (b) An unweighted graph
(a) Mark 3 to show the correct graph. (c) A weighted graph
Try question 10 in Formative Zone 5.1
Directed graph Undirected graph
Give your justification. Identify and draw subgraphs and trees
(b) Hence, draw a diagram to represent the
graph. 1. Subgraph of a graph is the graph consisting of
Solution: the particular vertex and edge of the original
graph.
(a) Directed graph 3
{(B, C)} and {(C, B)} are directed edges that BRILLIANT Tips
connect vertex B and vertex C.
(b) 1. If H is the subgraph of graph G, then
C (a) the vertices of H are also the vertices of G,
A (b) the edges with its two vertices of H are also
the edges with its two vertices of G.
2. A subgraph may have shapes that are different
D B from the original graph but its vertices and edges
must be the same.
Try question 9 in Formative Zone 5.1 3. Each graph is a subgraph of itself.

2. Difference between weighted graph and B C B
unweighted graph. B
Graph A C
B A C
C Subgraphs A
Weighted graph Unweighted graph A of graph B
5 B B C
2 C C B A
7 9 A B A C
C B
B A
Each edge is associated Each edge is not A C C
with a number called associated with a A A
weight. number.

5.1.2 5.1.3 97

ENG05 Spotlight Matematik F4.indd 97 14/01/2021 9:56 PM