Page 19 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4 Mathematics Chapter 5 Network in Graph Theory

Example 11 Example 13

The diagram on the right shows D C The diagram below shows a graph G.
graph G. D
Determine whether each of the
following is a subgraph of G. A B C
(a) (b) C
D
B B A E
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Graph H has the following vertices and edges.
Determine whether H is a subgraph of G. Give
A B D your justification.
(c) (d) A (a) Vertices of H = {A, B, C, D}
D C B
Edges of H = {(A, B), (A, C), (B, C), (C, D)}
CHAP. (b) Vertices of H = {A, B, C, E}
Edges of H = {(A, B), (A, C), (C, E)}
5 A B D Solution:
Solution: (a) H is a subgraph of G because the vertices and
(a) A subgraph of G. edges of H are the same as G.
(b) A subgraph of G although its shape is different (b) H is not a subgraph of G because {(C, E)} is
from G but it has the same vertices {B, C, D} not an edge of G.
and edges {(B, C), (B, D), (C, D)}. Try question 13 in Formative Zone 5.1
(c) Not a subgraph of G because G does not
contain the edge {(A, D)}.
(d) A subgraph of G although its shape is different
from G but it has the same vertices {A, B, D}
and edge {(B, D)}. Example 14
Try question 11 in Formative Zone 5.1
Draw four possible subgraphs for each of the
following graphs G.
Example 12 (a) (b)
The diagram below shows a directed graph G. D E
D D
E C
C F A B
A B E
B
Solution:
A C
(a)
State whether each of the following directed
graphs is a subgraph of G. Give your justification. D D E D E D
(a) A (b)
A C C
D B E F C F F
A B B
E
(b)
C D D D D
Solution: C B C C
A B
(a) Not a subgraph of G because the edge
{(C, D)} is not in its graph. E E E E
(b) A subgraph of G because the vertices {A, B,
D, E} and edges {(A, B), (A, E), (D, E), (E, D)} Try question 14 in Formative Zone 5.1
are the same as graph G.
Try question 12 in Formative Zone 5.1

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ENG05 Spotlight Matematik F4.indd 98 14/01/2021 9:56 PM