MAT F4 KSSM Network and Graph Theory

CHAPTER 5:
NETWORK IN GRAPH
THEORY

MATHEMATICS FORM 4

KSSM

5.1 NETWORK

RELATIONSHIP BETWEEN NETWORK

AND GRAPH TEXTBOOK
Page 130

GRAPH NETWORK

➢ Series of dots which either linked or not ➢ Part of graphs with the vertices and edges
linked to one another by lines having their own characteristics.

➢ DOTS are known as VERTEX ➢Has many-to-many relation

➢ LINES joining the vertices known as EDGE Abu

Alia
Asri

NOTATION IN GRAPH TEXTBOOK
Page 131

SIMPLE State the number of vertices, edges and the sum of
GRAPH degrees for the following simple graph

Has no loops and Number of vertices:
no multiple edges = 1,2,3,4,5,6,7
= 7
A
Number of edges
D
= 1,7 , 7,2 , 2,6 , 6,3 , 3,4 , 3,5 , 4,5
B
= 7
C
Number of degrees:

Sum of degrees: 1 = 1
=2 (2) = 2
=2(7) (3) = 3
=14 (4) = 2
5 = 2

6 = 2

7 = 2

Sum of degrees = 14

TEXTBOOK
Page 131

WHAT ARE
MULTIPLE EDGES
AND LOOPS OF

GRAPHS??

LET’S CHECK IT
OUT

MULTIPLE EDGES MULTIPLE EDGES LOOP

Edges:

= , , , , , , , , , , , , , , ,

Number of edges: = 8 Number of degrees:
Number of degrees = 2 = 2 8 = 16 = 3
( ) = 5
( ) = 3
( ) = 5

Sum of degrees = 16

DRAWING GRAPH

1. Draw vertices
2. Draw edges according to

questions given

23 2 34

14

15
6

2 34

5
6 1 65

DRAWING GRAPH

1. Draw vertices
2. Draw edges according to

questions given

Q
PR

S

DETERMINE A GRAPH CAN BE DRAWN
OR NOT

Must be even number

Sum of degrees =

DEFINITION OF GRAPH AND NETWORK
IMPORTANT NOTATION IN GRAPHS AND NETWORKS
SIMPLE GRAPHS, MULTIPLE EDGES AND LOOPS
DRAWING GRAPHS FROM GIVEN INFORMATIONS

CHAPTER 5:
NETWORK IN GRAPH
THEORY

MATHEMATICS FORM 4

KSSM

5.1 NETWORK

DIRECTED VS UNDIRECTED GRAPH TEXTBOOK
Page 135

Order of DIRECTED UNDIRECTED
vertices GRAPH GRAPH

Written Not
according important
to direction

Directed graphs:
= +

where is vertices in the graph

TEXTBOOK
Page 137

WEIGHTED VS UNWEIGHTED GRAPHS

EXAMPLES MUST REMEMBER:
DIRECTION IS IMPORTANT
= , , , , ,
= { , , , , , , , , , , , , , } IN DIRECTED GRAPHS

Q S

>R

P

> T

U

EXAMPLES TIPS:
START WITH THE LEAST ONE
Q
P R

S

EXAMPLES

(i) → → ∶ 130 + 65 = 195 (ii) → → ∶ 2.6 + 0.75 = 3.35 hours
→ → → ∶ 50 + 45 + 65 = 160 → → ∶ 1 + 0.75 + 1.4 = 3.15 hours
→ ∶3 hours
→ → → →

COMPARE AND CONTRAST BETWEEN
DIRECTED AND UNDIRECTED GRAPHS

COMPARECONTRAST BETWEEN
WEIGHTED AND UNWIGHTED GRAPHS

DRAW DIRECTED GRAPHS

SOLVE PROBLEMS INVOLVING
WEIGHTED GRAPHS

Title Lorem Ipsum

LOREM IPSUM DOLOR SIT AMET, NUNC VIVERRA IMPERDIET ENIM. PELLENTESQUE HABITANT MORBI
CONSECTETUER ADIPISCING ELIT. FUSCE EST. VIVAMUS A TELLUS. TRISTIQUE SENECTUS ET NETUS.