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Unit 8 Test and BMK Review 1

Total questions: 53

Worksheet time: 1hrs 25mins

Name
Class
Date
1.

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

a)

Regions

b)

Vertices

c)

Edges

d)

Paths

2.
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
3.
Circuits start and stop at 
a)
same vertex
b)
different vertices
4.

Does this graph have a Euler's Circuit?

a)

Yes

b)

No

5.
How do we quickly determine if a graph will have a Euler's Circuit? 
a)
All even degree verticies
b)
Exactly 2 odd degree verticies
c)
Every Vertex will be used once
d)
I have no clue
6.

Is the following graph connected or disconnected? Explain why or why not.

a)

Connected because all vertices are even.

b)

Connected because one can get from one vertex to every other vertex on the graph

c)

Disconnected because all vertices are even

d)

Disconnected because one can NOT get from one vertex to every other vertex.

7.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I and II

8.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I and II

9.

Which of the graphs below have Euler circuits?

a)

I only

b)

II only

c)

Both I and II

d)

Neither I or II

10.

What is the degree of vertex A in the graph ?

a)

3

b)

5

c)

7

d)

11

11.

Is the following graph connected?

a)

Yes

b)

No

12.

Can a disconnected graph be an Euler Path or Circuit?

a)

No

b)

Yes

13.
Which of the following is false?
a)
Euler Paths exist when there are exactly two vertices of odd degree.
b)
Euler circuits exist when the degree of all vertices are even.
c)
A graph with more than two odd vertices will never have an Euler Path or Circuit.
d)
A graph with one odd vertex will have an Euler Path but not an Euler Circuit.
14.

Does this graph have an Euler Path, Euler Circuit, both, or neither?

a)

Euler Path

b)

Euler Circuit

c)

Both

d)

Neither

15.
This graph will have a Euler's Path. 
a)
True
b)
False
16.
This graph will have a Euler's Circuit
a)
True
b)
False
17.

Which of the following would be an Euler Circuit?

a)

KLQPQOKLOMK

b)

KLQMPQOKNLOMK

c)

KLQMPQOK

d)

KMOLNKOQMK

18.
How do we quickly determine if the graph will have a Euler's Path
a)
All even degree verticies
b)
Exactly 2 odd degree verticies
c)
Each vertex will be used once
d)
I have no clue. 
19.

This graph has an Euler's Path.

a)

True

b)

False

20.

Vertex

a)

a line connecting two vertices

b)

a point

c)

an edge

d)

an edge that starts and ends at the same vertex

21.

Adjacent vertices

a)

are connected to every other vertex in the graph

b)

are connected by at least one edge

c)

are in a loop together

d)

make a multigraph

22.

A loop is when

a)

there is a path going from a vertex back to itself

b)

An edge that starts and ends at the same vertex

c)

if it were removed, the graph would be disconnected

d)

connects two vertices to each other

23.

A path is

a)

an edge that starts and ends at the same vertex

b)

a connection between two vertices

c)

a series of consecutive edges in which no edge is repeated

d)

a complete graph

24.

A graph is connected if

a)

Each vertex can reach any other vertex

b)

each vertex is adjacent to every other vertex

c)

All the vertices are odd

d)

the length of all the edges are equal

25.

What is the graph's Euler Path?

a)

SUTSTUT

b)

USTU

c)

USTUTS

d)

TUST

26.

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

27.
A Euler's or Hamiltonian Circuit end and start in the same place. 
a)
True
b)
False
28.
In a Hamiltonian Path or Circuit, you must use each edge. 
a)
True 
b)
False
29.
In a Hamiltonian Circuit or Path, you can only use each vertex once. 
a)
True
b)
False
30.
Does this graph have a Hamiltonian Circuit?
a)
True
b)
False
31.

In a Hamiltonian Path, you must

a)

Travel every edge once and only once, returning to where you started

b)

Travel to every vertex once and only once, returning to where you started

c)

Travel every edge once and only once, not returning to where you started

d)

Travel to every vertex once and only once, not returning to where you started

32.

A Hamiltonian Path Exists on this graph

a)

Yes

b)

No

33.

Select a Hamiltonian path:

a)

acfgebad

b)

dacfgeb

c)

acfdeb

d)

abegfc

34.

In the following graph, decide which of the following is true: (could be more than one)

a)

You can find a Hamiltonian Circuit if you travel 6, 4, 5, 1, 2, 3, 4, 6

b)

You can find a Euler Path if you travel 1, 5, 2, 3, 4, 6

c)

You cannot find a Hamiltonian Path

d)

You cannot find a Euler Path

35.

State whether you can find a Hamiltonian path, circuit or neither.

a)

Path

b)

Circuit

c)

Neither

d)

both

36.

Find the Hamiltonian Path (ignore direction of arrows)

a)

1, 3, 4, 3, 2

b)

1, 2, 3, 4

c)

2, 3, 4, 3, 1

d)

There is none

37.

What is the degree of vertex 4?

a)

3

b)

4

c)

5

d)

7

38.

Which two vertices are adjacent vertices?

a)

5 is adjacent to 6

b)

3 is adjacent to 6

c)

4 is adjacent to 1

d)

3 is adjacent to 2

39.

The graph is an example of a

a)

Path

b)

Cycle

c)

Circuit

d)

Complete Graph

40.

Which vertices are adjacent to E?

a)

B and C

b)

B, C, D, and A

c)

B

d)

A, B, C, D, F, G

41.

Tina, Jessie, John, Bill, and Andy are all members of the social networking website Facebook. The site allows members to be “friends” with each other. It turns out that Bill and John are friends, as are Tina and Andy. Jessie is friends with everyone. Who is "E" ?

(a)  

42.

State the number of vertices.

a)

14

b)

3.5

c)

7

d)

5

43.

State the number of edges.

a)

18

b)

7

c)

9

d)

6

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.

Starting at node S, what is the minimum cost to reach node G?

a)

S-A-B-F-G

b)

S-A-B-C-G

c)

S-A-B-C-H-G

d)

S-A-B-C-E-H-G

47.

Starting at node S, what is the value of the shortest path to node G?

(a)  

48.

Which of the following is the cheapest route to visit each city using the “Brute Force Method” starting from A and ending at A.

a)

ACDBA, $900

b)

ABCDA, $970

c)

ACBDA, $960

49.

Katherine is using an online ride service to start from her home (vertex A) visit 3 consecutive destinations (B, C, D) and return home (vertex A). She first obtained all of the prices of traveling between locations and then, using the “Brute Force Method” she created this diagram..

Which graph below matches the diagram above?

a)

b)

c)

50.

Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with vertex ‘A’ and using the Nearest Neighbor Algorithm.

a)

ABCDA, $960

b)

ACDBA, $900

c)

ACBDA, $960

d)

None of the Above

51.

Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with vertex ‘A’ and using the Nearest Neighbor Algorithm.

a)

ABCDA, $880

b)

ABDCA, $890

c)

ACDBA, $890

52.

Which of the following is the cheapest route to visit each city using the “Brute Force Method” starting from A and ending at A.

a)

ACDBA, $900

b)

ABCDA, $970

c)

ACBDA, $960

53.

Katherine is using an online ride service to start from her home (vertex A) visit 3 consecutive destinations (B, C, D) and return home (vertex A). She first obtained all of the prices of traveling between locations and then, using the “Brute Force Method” she created this diagram..

Which graph below matches the diagram above?

a)

b)

c)

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