Page 36 - Hybrid PBD 2022 Tg 4 - Matematik

Matematik Tingkatan 4 Bab 5 Rangkaian dalam Teori Graf
5. Tentukan sama ada suatu graf boleh dilukis berdasarkan bilangan darjah yang diberi. SP 5.1.1 TP2
Determine whether a graph can be drawn based on the number of degrees given.

3, 2, 2, 2, 2
Tip Penting
Jumlah darjah / Sum of degrees = 3 + 2 + 2 + 2 + 2
=11 Suatu graf boleh dilukis apabila jumlah darjah
adalah genap.
Jumlah darjah ialah ganjil, maka graf tidak boleh dilukis A graph can be drawn when the sum of degrees is even.
Sum of degrees is odd, thus the graph cannot be drawn.

(a) 3, 2, 2, 2, 2, 1, 3 (b) 1, 3, 2, 2, 1, 2, 3
Jumlah darjah / Sum of degrees Jumlah darjah / Sum of degrees
= 3 + 2 + 2 + 2 + 2 + 1 + 3 =15 = 1 + 3 + 2 + 2 + 1 + 2 + 3 =14
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Jumlah darjah ialah ganjil, maka graf tidak boleh Jumlah darjah ialah genap, maka graf boleh
dilukis. dilukis
Sum of degrees is odd, thus the graph cannot be drawn. Sum of degrees is even, thus the graph can be drawn.

6. Lukis graf terarah mengikut maklumat yang diberikan. SP 5.1.2 TP3
Draw a directed graph based on the given information.

(a) (i) V = {P, Q, R, S}
(i) V = {P, Q, R, S, T} E = {(P, Q), (Q, R), (P, R), (R, S)}
E = {(P, Q), (P, R), (Q, S), (R, Q), (R, S), (S, T)}
(ii) Mempunyai satu gelung di S dan PQ ialah
(ii) Mempunyai satu gelung di bucu Q dan QR berbilang tepi dengan keadaan
ialah berbilang tepi dengan keadaan There is a loop at vertex S and PQ is a multiple edges such
There is a loop at vertex Q and QR is a multiple edges such that
that d in (P) = 1, d out (P) = 2
d in (P) = 0, d out (P) = 2 Graf Terarah dan d in (Q) = 4, d out (Q) = 0
d in (Q) = 4, d out (Q) = 2 Graf Tak Terarah d in (R) = 1, d out (R) = 1
d in (R) = 2, d out (R) = 2 VIDEO Directed and d in (S) = 1, d out (S) = 4
Undirected Graph
d in (S) = 1, d out (S) = 2
d in (T) = 1, d out (T) = 0 (i) (ii)
P S
(i) (ii) S R
P Q P Q

P Q
Q R
R S T R S T

(b) (i) V = {P, Q, R, S, T, U, V}
E = {(Q, P), (Q, R), (R, U), (R, S), (U, S), (U, V), (S, T), (T, V)}
(ii) Mempunyai satu gelung di R. TV dan UV ialah berbilang tepi dengan keadaan
There is a loop at Vertex R. TV and UV are multiple edges such that
d in (R) = 1, d out (R) = 3
d in (S) = 2, d out (S) = 1
d in (T) = 2, d out (T) = 1
d in (U) = 1, d out (U) = 3
d in (V) = 3, d out (V) = 1
(i) S T (ii) S T

R R
U V U V

Q P

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05 Hybrid PBD Mate Tg4.indd 66 22/10/2021 5:49 PM