Page 17 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4 Mathematics Chapter 5 Network in Graph Theory

1. Difference between directed graph and
BRILLIANT Tips undirected graph.
Graph
In a graph that has loops and multigraph, the degree
of a vertex is determined in the same way as simple
graphs. Directed graph Undirected graph

C C
Example 7
A B A B
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A, B, C and D are four vertices of a graph. Without
using graph, determine the degree for each of the
vertices with the following edges. D D
(a) {(A, B), (A, D), (B, D), (C, D), (C, D), (C, D)}
(b) {(A, D), (A, D), (B, B), (B, C), (B, C), (B, D), (C, C)} Each edge is marked Each edge is not
CHAP. Solution: with an arrow. marked with an arrow.
5 (a) Vertex A : 2 edges {(A, B), (A, D)} The edge A • • B The edge A • • B
º Degree (A) = 2 is written in the is written in the form
ordered pair (B, A). (A, B).
Vertex B : 2 edges {(A, B), (B, D)} (A, B) ≠ (B, A) (A, B) = (B, A)
º Degree (B) = 2
The edges of the graph The edges of the graph
Vertex C : 3 edges {(C, D), (C, D), (C, D)} are {(A, C), (A, D), are {(A, B), (A, C),
º Degree (C) = 3
(B, A), (B, C), (D, A)} (A, D), (A, D), (B, C)}
Vertex D : 5 edges {(A, D), (B, D), (C, D), (C, D),
(C, D)} BRILLIANT Tips
º Degree (D) = 5
(b) Vertex A : 2 edges {(A, D), (A, D)}
º Degree (A) = 2 1. For the directed graph, (A, A) represents a directed
loop.
Vertex B : 4 edges {(B, B), (B, C), (B, C), (B, D)}
º Degree (B) = 4 or
Vertex C : 3 edges {(B, C), (B, C), (C, C)} A A
º Degree (C) = 3 2. For the undirected graph, (A, A) represents an
undirected loop.
Vertex D : 3 edges {(A, D), (A, D), (B, D)}
º Degree (D) = 3
A
Try question 7 in Formative Zone 5.1

Example 8
BRILLIANT Tips Match the following.
(a)
The degree of a vertex is found by determining the
number of edges that involve the vertex.

Directed graph
Compare and contrasting (b)
(i) directed graphs and undirected graphs
(ii) weighted graphs and unweighted graphs

Undirected
(c)
graph

96 5.1.1 5.1.2

ENG05 Spotlight Matematik F4.indd 96 14/01/2021 9:56 PM