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Worksheets

Network in Graph Theory

Total questions: 25

Worksheet time: 13mins

Name
Class
Date
1.

State the number of vertices.

a)

14

b)

3.5

c)

7

d)

5

2.

State the number of edges.

a)

18

b)

7

c)

9

d)

6

3.

Determine the sum of degrees.

a)

16

b)

8

c)

4

d)

13

4.

Determine the n(E) for this graph with multiple edges and loops.

a)

8

b)

20

c)

5

d)

10

5.

Determine the sum of degrees.

a)

4

b)

8

c)

16

d)

32

6.

Determine n(E).

a)

7

b)

12

c)

14

d)

6

7.

State Σ d(v)

a)

4

b)

8

c)

16

d)

32

8.

State Σd(V) .

a)

5

b)

7

c)

10

d)

14

9.

Determine n(V).

a)

4

b)

8

c)

5

d)

10

10.

Which of the statements below is not true

a)

V = {P, Q, R, S, T, U}

b)

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

c)

d(R) = 3

d)

sum of degree = 18

11.

Which of the following statements in not true?

a)

V={ P, Q, R, S, T, U}

b)

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

c)

d(P) = 3

d)

sum of degree = 14

12.

The following undirected graph shows six houses in a village. A salesperson needs to visit all

the houses starting from house A and finishing at house F. Calculate the shortest distance in km.

a)

3.05

b)

3.08

c)

3.30

d)

3.68

13.

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

a)

Regions

b)

Vertices

c)

Edges

d)

Paths

14.

An edge that begins and ends at the same vertex.

a)

Multiple edges

b)

Vertices

c)

Loop

d)

Node

15.

Links that connect the same two vertices to one another.

a)

Multiple edges

b)

Vertices

c)

Loop

d)

Nodes

16.

When the edges have a numerical representation (to indicate length, time, capacity etc.).

a)

Multiple edges

b)

Weighted graph

c)

Complete graph

d)

Directed graph

17.

No arrows are shown on the edges.

a)

Directed graph

b)

Weighted graph

c)

Simple graph

d)

Undirected graph

18.

An undirected and unweighted graph with no multiple edges.

a)

Undirected graph

b)

Unweighted graph

c)

Incomplete graph

d)

Simple graph

19.

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)

A > C > D > E

b)

A > B > C > E

c)

A > D > E

d)

A > B > E

20.

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

a)

It must be directed.

b)

It must be undirected.

c)

It must have at least one vertex.

d)

It must have no multiple edges.

21.

Which one is NOT a subgraph of the above graph?

a)
b)
c)
d)
22.

Determine the number of vertices and sum of degrees.

a)

8,16

b)

8,8

c)

6,4

d)

8,13

23.

When the edges have a numerical representation (to indicate length, time, capacity etc.).

a)

Multiple edges

b)

Weighted graph

c)

Complete graph

d)

Directed graph

24.

The directed weighted graph on the right shows

the prices of tickets and the travel times for some

choices of flights of a private airline. Vertex S is the

destination of the flight from vertex P. Vertex Q and

vertex R are the transit airports. The transit time at

each of the airports is 45 minutes. Which one is the most economical route?

a)

P > Q > R > S

b)

P > R > S

c)

P > Q > S

d)

P > S

25.

The directed weighted graph on the right shows

the prices of tickets and the travel times for some

choices of flights of a private airline. Vertex S is the

destination of the flight from vertex P. Vertex Q and

vertex R are the transit airports. The transit time at

each of the airports is 45 minutes. Which route takes the shortest time?

a)

P > Q > R > S

b)

P > R > S

c)

P > Q > S

d)

P > S