Quiz about Question Bank Discrete Math Graph Theory

Question 1

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

Accepted Answer

Edges

Answer

Regions

Answer

Vertices

Answer

Paths

Question 2

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

Accepted Answer

Euler Circuit

Answer

Euler Path

Question 3

Circuits start and stop at

Accepted Answer

same vertex

Answer

different vertices

Question 4

This graph will have a Euler's Circuit

Accepted Answer

True

Answer

False

Question 5

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

Accepted Answer

All even degree verticies

Answer

Exactly 2 odd degree verticies

Answer

Every Vertex will be used once

Answer

I have no clue

Question 6

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

Accepted Answer

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

Answer

Connected because all vertices are even.

Answer

Disconnected because all vertices are even

Answer

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

Question 7

Which of the graphs below have Euler circuits?

Accepted Answer

II only

Answer

I only

Answer

Both I and II

Answer

Neither I and II

Question 8

Which of the graphs below have Euler circuits?

Accepted Answer

I only

Answer

II only

Answer

Both I and II

Answer

Neither I and II

Question 9

Which of the graphs below have Euler circuits?

Accepted Answer

Both I and II

Answer

I only

Answer

II only

Answer

Neither I or II

Question 10

What is the valence (degree) of vertex A in the graph ?

Accepted Answer

5

Answer

3

Answer

7

Answer

11

Question 11

Is the following graph connected?

Accepted Answer

No

Answer

Yes

Question 12

Euler paths must touch

Accepted Answer

all edges

Answer

all vertices

Question 13

Which of the following is false?

Accepted Answer

A graph with one odd vertex will have an Euler Path but not an Euler Circuit.

Answer

Euler Paths exist when there are exactly two vertices of odd degree.

Answer

Euler circuits exist when the degree of all vertices are even.

Answer

A graph with more than two odd vertices will never have an Euler Path or Circuit.

Question 14

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

Accepted Answer

Both

Answer

Euler Path

Answer

Euler Circuit

Answer

Neither

Question 15

This graph will have a Euler's Path.

Accepted Answer

False

Answer

True

Question 16

This graph will have a Euler's Circuit

Accepted Answer

True

Answer

False

Question 17

Identify the Euler's Circuit

Accepted Answer

KLQMPQOKNLOMK

Answer

KLQPQOKLOMK

Answer

KLQMPQOK

Answer

KMOLNKOQMK

Question 18

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

Accepted Answer

All even degree verticies

Answer

Exactly 2 odd degree verticies

Answer

Every Vertex will be used once

Answer

I have no clue

Question 19

How do we quickly determine if the graph will have a Euler's Path

Accepted Answer

Exactly 2 odd degree verticies

Answer

All even degree verticies

Answer

Each vertex will be used once

Answer

I have no clue.

Question 20

Euler paths must touch

Accepted Answer

all edges

Answer

all vertices

Question 21

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

Accepted Answer

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

Answer

Connected because all vertices are even.

Answer

Disconnected because all vertices are even

Answer

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

Question 22

If a graph of four vertices has a vertex with valence (degree) 0, then the graph is not connected.

Accepted Answer

True

Answer

False

Question 23

Which of the graphs below have Euler paths?

Accepted Answer

Both I and II

Answer

I only

Answer

II only

Answer

Neither I and II

Question 24

Which of the graphs below have Euler paths?

Accepted Answer

Both I and II

Answer

I only

Answer

II only

Answer

Neither I or II

Question 25

What is the valence (degree) of vertex F in the graph ?

Accepted Answer

4

Answer

3

Answer

5

Answer

11

Question 26

Which of the following graphs is isomorphic to

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 27

Circuits start and stop at

Accepted Answer

same vertex

Answer

different vertices

Question 28

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

Accepted Answer

Euler Circuit

Answer

Euler Path

Question 29

Euler paths must touch

Accepted Answer

all edges

Answer

all vertices

Question 30

Find a Hamilton circuit from D using the Nearest Neighbor Alogrithm.

Accepted Answer

DABECD

Answer

DAEBCD

Answer

DBEACD

Answer

DCABED

Question 31

What is the weight of edge AC?

Accepted Answer

5

Answer

6

Answer

3

Answer

11

Question 32

What is the degree of vertex 4?

Accepted Answer

3

Answer

4

Answer

5

Answer

7

Question 33

Which is an example of a disconnected graph?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Answer

None are disconnected graphs

Question 34

An edge that begins and ends at the same vertex.

Accepted Answer

Loop

Answer

Multiple edges

Answer

Vertices

Answer

Node

Question 35

A Hamilton Circuit must touch every __________ once and only once

Accepted Answer

Vertex

Answer

Edge

Answer

Loop

Answer

Degree

Question 36

Which of the graphs below is a spanning tree of this connected graph?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 37

Which vocabulary term is illustrated through the diagram?

Accepted Answer

Minimal Spanning Tree

Answer

Four Color Theorem

Answer

Cycle

Answer

Vertices

Question 38

The graph represents the following vocabulary term.

Accepted Answer

Cycle

Answer

Path

Answer

Complete Graph

Answer

Complete Bipartite Graph

Question 39

The graph is an example of a

Accepted Answer

Complete Graph

Answer

Path

Answer

Cycle

Answer

Complete Bipartite Graph

Question 40

Which vocabulary term describes the graph?

Accepted Answer

path

Answer

circuit

Answer

complete graph

Answer

polygon

Question 41

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

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 42

How many leaf are there in the tree?

Accepted Answer

3

Answer

1

Answer

4

Answer

7

Question 43

Find the Hamiltonian Path

Accepted Answer

There is none

Answer

1, 3, 4, 3, 2

Answer

1, 2, 3, 4

Answer

2, 3, 4, 3, 1

Question 44

Which two vertices are adjacent vertices?

Accepted Answer

3 is adjacent to 2

Answer

5 is adjacent to 6

Answer

3 is adjacent to 6

Answer

4 is adjacent to 1

Question 45

The graph is an example of a

Accepted Answer

Complete Graph

Answer

Path

Answer

Cycle

Answer

Circuit

Question 46

Which vertices are adjacent to E?

Accepted Answer

B and C

Answer

B, C, D, and A

Answer

B

Answer

A, B, C, D, F, G

Question 47

Which graph is not a complete graph?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 48

By looking at the pattern of the numbers in the table, determine the number of edges for a complete graph to be drawn from 9 nodes given.

Accepted Answer

36

Answer

28

Answer

45

Answer

55

Question 49

If the number of edges of a complete graph can be drawn from n nodes given is 91. What is the value of n?

Accepted Answer

14

Answer

12

Answer

13

Answer

15

Question 50

State the number of vertices.

Accepted Answer

7

Answer

14

Answer

3.5

Answer

5

Question 51

State the number of edges.

Accepted Answer

9

Answer

18

Answer

7

Answer

6

Question 52

Determine the sum of degrees.

Accepted Answer

16

Answer

8

Answer

4

Answer

13

Question 53

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

Accepted Answer

Edges

Answer

Regions

Answer

Vertices

Answer

Paths

Question 54

Links that connect the same two vertices to one another.

Accepted Answer

Parallel edges

Answer

Vertices

Answer

Loop

Answer

Nodes

Question 55

Which of the following is not a path from D to A/

Accepted Answer

All of the above are paths from D to A

Answer

DCA

Answer

DEDCCA

Answer

DCCA

Answer

DECDA

Question 56

What is the degree of Vertex D?

Accepted Answer

5

Answer

1

Answer

2

Answer

3

Answer

4

Question 57

Which of the following is possible for the graph?

Accepted Answer

None of the above

Answer

Euler Path

Answer

Euler Circuit

Answer

Hamilton Path

Answer

Hamilton Circuit

Question 58

Which is possible for the graph?

Accepted Answer

Hamilton Path

Accepted Answer

Hamilton Circuit

Answer

Euler Path

Answer

Euler Circuit

Answer

None of the above

Question 59

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

Accepted Answer

Euler Circuit

Answer

Euler Path

Question 60

Circuits start and stop at

Accepted Answer

same vertex

Answer

different vertices

Question 61

What is the valence of vertex A in the graph ?

Accepted Answer

5

Answer

3

Answer

7

Answer

11

Question 62

What is the valence of vertex F in the graph ?

Accepted Answer

4

Answer

3

Answer

5

Answer

11

Question 63

Use ALL, SOME or NO to complete the sentence.

______Euler paths are Euler Circuits.

Accepted Answer

SOME

Answer

ALL

Answer

NO

Question 64

Use ALL, SOME or NO to complete the sentence.

______Euler Circuits are Euler Paths

Accepted Answer

ALL

Answer

SOME

Answer

NO

Question Bank Discrete Math Graph Theory

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