Page 34 - Hybrid PBD 2022 Tg 4 - Matematik

Matematik Tingkatan 4 Bab 5 Rangkaian dalam Teori Graf

(a) M N X Y (b) B e 1 C E e 6 F

e e
e 2 e 3 5 7 e 9

W Q A e 4 D e 8 G e 10 H

V = {M, N, W, Q, X, Y} V = {A, B, C, D, E, F, G, H}
n(V) = 6 n(V) = 8
E = {(M, N), (N, W), (N, Q), (W, Q), (Q, X), (X, Y)} E = {e 1 , e 2 , e 3 , e 4 , e 5 , e 6 , e 7 , e 8 , e 9 , e 10 }
n(E) = 6 n(E) = 10
Jumlah bilangan darjah / Sum of degrees, Jumlah bilangan darjah / Sum of degrees,
Σd(v) = 2n(E) = 12 Σd(v) = 2n(E) = 20

2. Tentukan V, n(V), E, n(E) dan jumlah bilangan darjah bagi graf berbilang tepi dan gelung. SP 5.1.1 TP2
Determine V, n(V), E, n(E) and sum of degrees for the following graphs with multiple edges and loops.

A B

Tip Penting
Gelung ialah apabila suatu tepi bermula dan
C D berakhir pada bucu yang sama. Bilangan
darjah untuk setiap gelung ialah 2.
V = {A, B, C, D} A loop is when an edge starts and ends at the same
n(V) = 4 vertex. The number of degrees for each loop is 2.
E = {(A, B), (A, C), (A, C), (C, D), (B, D), (D, D)}
n(E) = 6 Penerbitan Pelangi Sdn Bhd. All Rights Reserved
Jumlah bilangan darjah / Sum of degrees, Σd(v) = 2n(E)
= 12
Darjah di Bucu A / Degree of Vertex A = 3
Darjah di Bucu C / Degree of Vertex C = 3
Darjah di Bucu B / Degree of Vertex B = 2
Darjah di Bucu D / Degree of Vertex D = 4

(a) P Q (b) A C

S R
B D
T
V = {P, Q, R, S, T} V = {A, B, C, D}
n(V) = 5 n(V) = 4
E = {(P, Q), (P, R), (P, S), (P, P), (Q, R), (Q, R), (S, R), E = {(A, B), (A, C), (B, C), (B, C), (B, B), (B, D), (C, C),
(S, T), (R, T), (T, T)} (C, D), (D, D)}
n(E) =10 n(E) = 9
Jumlah bilangan darjah / Sum of degrees, Jumlah bilangan darjah / Sum of degrees,
Σd(v) = 2n(E) = 20 Σd(v) = 2n(E) = 18
Darjah di Bucu P / Degree of Vertex P = 5 Darjah di Bucu A / Degree of Vertex A = 2
Darjah di Bucu S / Degree of Vertex S = 3 Darjah di Bucu B / Degree of Vertex B = 6
Darjah di Bucu Q / Degree of Vertex Q = 3 Darjah di Bucu C / Degree of Vertex C = 6
Darjah di Bucu T / Degree of Vertex T = 4 Darjah di Bucu D / Degree of Vertex D = 4
Darjah di Bucu R / Degree of Vertex R = 5

E-pop Quiz
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05 Hybrid PBD Mate Tg4.indd 64 22/10/2021 5:49 PM