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Unit 4 Q1

Total questions: 23

Worksheet time: 12hrs 30mins

Name
Class
Date
1.

Circuits start and stop at

a)

the same vertex

b)

different vertices

c)

the edge

d)

Never stop

2.

This graph will have an Euler Circuit.

a)

True

b)

False

3.

How do we quickly determine if a graph will have an Euler Circuit? 

a)

All even degree vertices

b)

Exactly 2 odd degree vertices

c)
Every Vertex will be used once
d)
I have no clue
4.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I and II

5.

What is the degree of vertex A in the graph ?

a)

3

b)

5

c)

7

d)

11

6.

This graph will have an Euler Path.

a)

True

b)

False

7.

What is the degree of vertex F in the graph ?

a)

3

b)

4

c)

5

d)

11

8.

To be classified as an Euler path, the vertices of a graph must....

a)

All be odd degrees.

b)

all be even degrees.

c)

Have 2 odd degrees.

d)

Have 2 even degrees.

9.
Euler paths must touch
a)
all edges
b)
all vertices
10.

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

a)

Regions

b)

Vertices

c)

Edges

d)

Paths

11.

Is this a HAMILTONIAN

Circuit, Path, or Neither?

a)

Circuit

b)

Path

c)

Neither

12.

Is this a HAMILTONIAN

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

13.

Is this a HAMILTONIAN

Circuit, Path, or Neither

a)

Circuit

b)

Path

c)

Neither

14.

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

a)

5

b)

7

c)

9

d)

11

15.
True or false: With Hamilton circuits, every edge must be used. With Euler circuits, every vertex must be used.
a)
True
b)
False
16.

The graph shown contains NO cycles.

a)

True

b)

False

17.

The graph shown contains NO cycles.

a)

True

b)

False

18.

The number of vertices in a minimum spanning tree that has 12 edges is 

a)
10
b)
11
c)
12
d)
13
19.

A Hamiltonian cycle is

a)

A cycle that includes every vertex

b)

A cycle that includes every vertex more than once

c)

A cycle that includes every edge

d)

A cycle that includes every edge more than once

20.
Does this graph have a Hamiltonian Circuit?
a)

Yes

b)

No

21.

Use the table to to find the most efficient network (i.e. lowest total).

a)

26

b)

20

c)

28

d)

24

22.

Make an efficient network (lowest total)

a)

50

b)

200

c)

48

d)

61

23.

Turn this Euler Path into an Euler Circuit. What is the original number and the new number?

a)

Original: 27

New: 34

b)

Original: 27

New: 35

c)

Original: 27

New: 37

d)

Original: 27

New: 8