Form 4 : Network in Graph Theory

Calculate the sum of degrees of the graph.

• 6

• 10

• 12

• 20

The diagram shows a simple graph.

What is the total number of trees that drawn based on the graph?

• 1

• 2

• 3

• 4

The diagram shows a graph with loops and multiple edges.

Which of the following is not true?

• d(P) = 4

• d(Q) = 3

• d(R) = 4

• $\ \Sigma d\left(v\right)=12$

The diagram shows a graph with a loop and multiple edges.

Calculate n(E).

• 6

• 7

• 8

• 9

The diagram shows an undirected weighted graph.

Aminah draws a subgraph with 7 vertices and 6 edges based on the graph. What is the minimum total weight of the subgraph?

• 9

• 10

• 11

• 12

Which of the following is not a possible list of the degrees of the vertices of a graph?

• 1,1,2,3,3

• 1,2,2,3,4

• 1,2,3,3,5

• 1,2,2,3,5

Which of the statements below is not true?

• V = {P, Q, R, S, T, U}

• E = {(R,S), (S,T), (T,U), (U,P), (P,Q)}

• d(R) = 3

• sum of degree = 18

Which of the following statements in not true?

• V={ P, Q, R, S, T, U}

• E= {(P,P), (P,R), (R,S), (S,T), (T,S), (R,Q), (Q,P)}

• d(P) = 3

• sum of degree = 14

Which of the following statements is not true?

• V = { P, Q, R, S, T}

• E = { (P,Q), (Q,R), (S,R), (S,T), (T,T), (P,S), (S,P)}

• d_in (T) = 2

• sum of degree = 14

The directed graph on the right shows the

roads connecting Lani’s house at A to the

school at E. Suggest the shortest route

that Lani can choose to cycle to school.

• A > C > D > E

• A > B > C > E

• A > D > E

• A > B > E