wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Graph Theory Check

Total questions: 68

Worksheet time: 48mins

Name
Class
Date
1.

Tracing all edges on a figure without picking up your pencil and repeating and starting and stopping in the same spot

a)

Euler Circuit

b)

Euler Path

2.

Circuits start and stop at

a)

same vertex

b)

different vertices

3.
This graph will have a Euler's Circuit
a)
True
b)
False
4.
How do we quickly determine if a graph will have a Euler's Circuit? 
a)

All even degrees

b)

Exactly 2 odd degrees

c)
Every Vertex will be used once
d)
I have no clue
5.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I and II

6.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I and II

7.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I or II

8.
This graph will have a Euler's Path. 
a)
True
b)
False
9.

Does this graph have an Euler Path, Euler Circuit, or just a vertex-edge graph?

a)
Euler Path
b)
Euler Circuit
c)

Vertex-Edge Graph

10.
Identify the Euler's Circuit
a)
KLQPQOKLOMK
b)
KLQMPQOKNLOMK
c)
KLQMPQOK
d)
KMOLNKOQMK
11.
How do we quickly determine if the graph will have a Euler's Path
a)

All even valences

b)

Exactly 2 odd valences

c)
Each vertex will be used once
d)
I have no clue. 
12.

Given the graph, ABCA is:

a)

Euler Circuit

b)

Euler Path

c)

Neither, it does not cover every edge

13.

Given the graph, ABDCA is

a)

Euler Circuit

b)

Euler Path

c)

Neither, it does not cover every edge

14.

Given the graph, ACDBC is:

a)

Euler Circuit

b)

Euler Path

c)

Neither, it does not cover every edge

15.

Which of the following is a Euler Path in the graph?

a)

DBACB

b)

CABD

c)

ACBD

d)

There is no Euler Path

16.

Which of the following is an Euler Circuit in the graph

a)

EABEDCE

b)

ABCDE

c)

DCED

d)

CEABC

17.

Which of the following is an Euler Circuit in the graph?

a)

0120

b)

1203401

c)

12034

d)

401204

18.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

19.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

20.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

21.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

22.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

23.

Identify each as a Hamiltonian

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

24.
a)

AECDB

b)

BDCEA

c)

CDABE

d)

DCBAE

25.

Which describes the edges of the graph?

a)

{A,B}, {A,C}, {A, E}, {B,C}, {B,E}

b)

A, B, C, D, E

c)

{A,B}, {A,C}, {A, E}, {B,C}, {B,E}, {C,D}

d)

{A,B}, {A,C}, {A, E}

26.

What are the dots in a graph called?

a)

Vertices

b)

Edges

c)

Euler Circuits

d)

Euler Paths

27.

What are the lines in a graph called?

a)

Vertices

b)

Edges

c)

Euler Circuits

d)

Euler Paths

28.

What is is called when you can go through every edge on a graph exactly once?

a)

Euler Circuit

b)

Euler Path

c)

Connected Graph

29.

What is is called when you can go through every edge on a graph exactly once and end back where you started?

a)

Euler Circuit

b)

Euler Path

c)

Connected Graph

30.

Does this graph have an Euler Circuit?

a)

Yes

b)

No

31.

Does this graph have an Euler Path?

a)

Yes

b)

No

32.

You can tell a graph has an Euler Circuit if it has no vertices with an ___________ degree.

a)

Odd

b)

Even

33.

The graph represents the following vocabulary term.

a)

Circuit

b)

Path

c)

Complete Graph

d)

Complete Bipartite Graph

34.

What is the weight of the shortest path from A to F?

a)

5

b)

7

c)

9

d)

11

35.

The degree of any vertex of graph is .... ?

a)

The number of edges incident with vertex

b)

Number of vertex in a graph

c)

Number of vertices adjacent to that vertex

d)

Number of edges in a graph

36.

Another name for a vertex is... ?

a)

Node

b)

Degree

c)

Valency

d)

Order

37.

Two vertices are _______ if there is a path between them.

a)

Connected

b)

Odd

c)

Even

d)

Weighted

38.

Which is an example of a disconnected graph?

a)
b)
c)
d)
e)

None are disconnected graphs

39.

The diagram shows a network. Find the degree of vertex B.

a)

4

b)

5

c)

6

d)

7

40.

Diagram shows a type of graph.

What is the type of graph?

a)

Weighted graph

b)

Directed graph

c)

Simple graph

d)

Tree

41.

What is the degree of Vertex D?

a)

1

b)

2

c)

3

d)

4

e)

5

42.

What is the weight of the shortest path from A to F?

a)

5

b)

7

c)

9

d)

11

43.

State the number of vertices.

a)

14

b)

3.5

c)

7

d)

5

44.

Determine the sum of degrees.

a)

16

b)

8

c)

4

d)

13

45.

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

a)

Regions

b)

Vertices

c)

Edges

d)

Paths

46.

An edge that begins and ends at the same vertex.

a)

Multiple edges

b)

Vertices

c)

Loop

d)

Node

47.

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

48.

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

49.

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

50.

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

51.

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

52.

Which of the following situations can be modelled as a weighted graph?

a)

Flight time from one location to the others

b)

The traffic flow at a junction

c)

The distance between tourist attractions in a city

d)

All of the above

53.

Which of the following is the shortest route from A to F?

a)

A, B, C, D, F

b)

A, B, C, E, F

c)

A, B, E, D, F

d)

A, B, E, F

54.

Based on the diagram , which of the following is the correct network from A to E?

a)

A, C, D, E

b)

A, D, C, E

c)

A, B, C, D

d)

A, C, B, E

55.

Diagram 1 shows a graph. Calculate the sum of degree.

a)

9

b)

12

c)

18

d)

20

56.

Diagram 2 shows a graph.

Which type of graph is represented by the graph?

a)

Unweighted directed graph

b)

Unweighted undirected graph

c)

Weighted directed graph

d)

Weighted undirected graph

57.

Find the most optimum path to travel from a to d.

a)

a --> b --> d

b)

a --> b --> c --> d

c)

a --> e --> d

d)

a --> d

58.

If there is an edge joining these two vertices then the graph is said to be ---------

a)

Adjacent

b)

Non adjacent

c)

Incident

d)

Non incident

59.

Find the size of a given graph ?

a)

4

b)

5

c)

6

d)

7

60.

Is the given graph is complete graph?

a)

Yes

b)

No

61.

The degree of any vertex of graph is .... ?

a)

The number of edges incident with vertex

b)

Number of vertex in a graph

c)

Number of vertices adjacent to that vertex

d)

Number of edges in a graph

62.

If I want to travel every edge once and I don't mind repeating vertices, I need to think...

a)

Bipartite graph

b)

Hamiltonian path

c)

Complete graph

d)

Eulerian circuit

63.

A path that starts and finishes at the same vertex.

a)

circuit

b)

path

c)

closed walk

d)

loop

64.

A trail that starts and finishes at the same vertex

a)

Open trail

b)

Closed trail

c)

Semi trail

d)

No trail

65.

Two vertices connected by a path that has only one edge.

a)

Adjacent vertices

b)

Parallel vertices

c)

Corresponding vertices

d)

Even vertices

66.

Which vertex has an even degree/order?

a)

A

b)

B

c)

C

d)

D

e)

E

67.

What is the degree of vertex 4?

a)

3

b)

4

c)

5

d)

7

68.

Number of edges of a tree of vertices 10 is ____

a)

10

b)

11

c)

9

d)

5

Similar Resources on Wayground

CH1: functions, domain & range, exponent laws, and order of operations

67 questions

CH1: functions, domain & range, exponent laws, and order of operations

quiz

Worksheet

•

8th - 12th Grade

Circle Slides M2

68 questions

Circle Slides M2

quiz

Worksheet

•

9th - 12th Grade

Math 3 Unit 1 Review

65 questions

Math 3 Unit 1 Review

quiz

Worksheet

•

11th - 12th Grade

Sem I Final Practice

68 questions

Sem I Final Practice

quiz

Worksheet

•

9th - 12th Grade

Graphing Quadratic Functions with Transformations

70 questions

Graphing Quadratic Functions with Transformations

quiz

Worksheet

•

9th - 12th Grade

Geometric Transformations Practice Test

67 questions

Geometric Transformations Practice Test

quiz

Worksheet

•

9th - 11th Grade

Interpreting histograms

70 questions

Interpreting histograms

quiz

Worksheet

•

9th Grade

Geometry Topic 5 Review

72 questions

Geometry Topic 5 Review

quiz

Worksheet

•

8th - 10th Grade