Deck 15: Graph Theory

Question 1

Determine whether the graph is connected or disconnected.

Answer 1

A

Question 2

Answer 2

D

Question 3

Answer 3

C

Question 4

Question 5

A)4 vertices; 4 edges
B)4 vertices; 3 edges
C)5 vertices; 4 edges
D)4 vertices; 5 edges

Question 6

Determine whether the graph is connected or disconnected.

Question 7

Question 8

Determine whether the graph is connected or disconnected.

Question 9

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 10

Question 11

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 12

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 13

Determine whether the graph is connected or disconnected.

Question 14

Question 15

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 16

Question 17

Question 18

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 19

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 20

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.

Question 21

Determine whether the graph is connected or disconnected.

Question 22

Determine how many components the graph has.

Question 23

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 5 vertices, one of degree 4, three of degree 3, and one of degree 1.

A)4 edges
B)7 edges
C)3 edges
D)8 edges

Question 24

Determine whether the graph is connected or disconnected.

Question 25

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 6 vertices, two of degree 2, three of degree 1, and one of degree 3.

A)20 edges
B)10 edges
C)5 edges
D)6 edges

Question 26

Determine how many components the graph has.

Question 27

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 5 vertices, three of degree 2 and two of degree 3.

A)12 edges
B)6 edges
C)9 edges
D)5 edges

Question 28

Determine how many components the graph has.

Question 29

Determine how many components the graph has.

Question 30

Determine how many components the graph has.

Question 31

Determine how many components the graph has.

Question 32

Determine how many components the graph has.

Question 33

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 4 vertices each of degree 2.

A)6 edges
B)16 edges
C)8 edges
D)4 edges

Question 34

Determine whether the graph is connected or disconnected.

Question 35

Determine how many components the graph has.

Question 36

Determine how many components the graph has.

Question 37

Determine how many components the graph has.

Question 38

Determine whether the graph is connected or disconnected.

Question 39

Determine whether the graph is connected or disconnected.

Question 40

Determine whether the graph is connected or disconnected.

Question 41

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 6 vertices, one of degree 5, three of degree 1, and two of degree 2.

A)8 edges
B)4 edges
C)6 edges
D)12 edges

Question 42

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 43

Determine whether the graph is a complete graph.

Question 44

Determine whether the graph is a complete graph.

Question 45

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 46

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 7 vertices, one of degree 6 and six of degree 1.

A)6 edges
B)7 edges
C)14 edges
D)13 edges

Question 47

Determine whether the graph is a complete graph.

Question 48

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 49

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 50

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 51

Determine whether the graph is a complete graph.

Question 52

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 53

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 54

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 55

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 8 vertices, two of degree 2, four of degree 3, and two of degree 1.

A)9 edges
B)6 edges
C)3 edges
D)18 edges

Question 56

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 57

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 7 vertices, one of degree 4, three of degree 3, and three of degree 1.

A)4 edges
B)8 edges
C)16 edges
D)12 edges

Question 58

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 10 vertices, three of degree 5, three of degree 3, two of degree 2, and two of degree 1.

A)18 edges
B)12 edges
C)11 edges
D)15 edges

Question 59

Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
A graph with 8 vertices, one of degree 4, three of degree 2, and four of degree 1.

A)6 edges
B)7 edges
C)14 edges
D)5 edges

Question 60

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.

Question 61

Determine whether the graph is a complete graph.

Question 62

Represent the following with a graph.

Question 63

Represent the following with a graph.

Question 64

Determine whether the graph is a complete graph.

Question 65

Solve the problem.
Six freshmen move into a dormitory suite at the beginning of the semester. In order to get
to know one another, they decide to have breakfast in pairs for the next few days, each
student having a different breakfast partner each day until each student has had breakfast
with all other students exactly once. Draw a graph with vertices representing students and
edges representing breakfast dates. How many breakfasts will occur? How many days will
the process take?

Question 66

There are 9 members on a baseball team. At the end of the game, each member of the team shakes hands with each member of the opposing team. How many handshakes occur?

A)40.5
B)162
C)81
D)9

Question 67

Determine whether the graph is a complete graph.

Question 68

Determine whether the graph is a complete graph.

Question 69

Determine whether the graph is a complete graph.

Question 70

Solve the problem.
A computer network is to be built by connecting two "server" computers to 6 "client"
computers. Each client computer is connected to each server by a single cable. Also, the
two servers are connected by a single cable. Draw a graph with vertices representing
computers and edges representing cables. How many cables are required? Is the graph of
the network a complete graph?

Question 71

Solve the problem.
Two schools play a tennis tournament. Each school has a team made up of 5 players, and
each player must play one match with each player of the opposing team. Draw a graph
with vertices representing players and edges representing matches. How many matches
will be played in the tournament?

Question 72

Represent the following with a graph.

Question 73

Determine whether the graph is a complete graph.

Question 74

James, Carl, Mark, Antonio, Phillip, and Brad are friends at college. Carl, Antonio and
Phillip have calculus together. Brad, Carl, and Mark have the same English composition
class. Draw a graph with vertices representing students and edges representing the relation
"take a common class". How many components does the graph have? Identify a subgraph
that is a complete subgraph with three vertices.

Question 75

James, Carl, Mark, Antonio, Phillip, and Brad are friends at college. James, Antonio and
Phillip have calculus together. Brad and Carl have the same English composition class.
Draw a graph with vertices representing students and edges representing the relation "take
a common class". How many components does the graph have? Identify a subgraph that is
a complete subgraph with three vertices.

Question 76

Represent the following with a graph.
Create a graph that models the bordering relationship among the states shown in the map. Use vertices to represent the states and edges to represent common borders.

Question 77

Seven family members are planning a picnic. They work out the details with a few phone calls. One family member has 5 conversations, two have 3 conversations, and one has only 1 conversation.
How many phone conversations are there?

A)9
B)12
C)6
D)18

Question 78

Solve the problem.
A psychology class decides to compare the social attitudes of students from urban and
rural backgrounds. Class members are divided into two groups: 5 students who grew up in
an urban setting and 3 students who grew up in a rural environment. Each member of a
group is to meet with each member of the other group one time, at which time the pair will
interview each other by asking questions about current social issues. After all the
interviews are completed, the students will compile the results and draw conclusions.
Draw a graph with vertices representing students and edges representing interviews. How
many interviews will there be?

Question 79

Solve the problem.
An internet user is participating simultaneously in one-on-one chat sessions with 5 other
people. Draw a graph with vertices representing users and edges representing chat
sessions. How many chat sessions are occurring?

Question 80

Ten police officers patrol in pairs. Two officers have each patrolled with 5 other officers, four officers have patrolled with 3 others, two have patrolled with 2 others, and two have patrolled with
Only 1 other officer. How many different patrol pairs have there been?

A)11
B)14
C)28
D)7