F4 Unit 5: Network in Graph Theory

A simple graph has no loops. What other property must a simple graph have?

• It must be directed.

• It must be undirected.

• It must have at least one vertex.

• It must have no multiple edges.

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 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

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

Determine the number of vertices and sum of degrees.

• 8,16

• 8,8

• 6,4

• 8,13

Determine the sum of degrees.

• 4

• 8

• 16

• 32

Determine n(E).

• 7

• 12

• 14

• 6

Determine n(V).

• 4

• 8

• 5

• 10

Choose the correct term to match each definition: Lines or curves that connect vertices.

• Regions

• Vertices

• Edges

• Paths

An edge that begins and ends at the same vertex.

• Multiple edges

• Vertices

• Loop

• Node