Question 1

Determine whether the graph is a complete graph.
-
A) $\mathrm { No }$
B) Yes

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 2

Represent the following with a graph.
-
A)

B)

C)

D)

Accepted Answer

The answer of Represent the following with a graph.
-
A)

B)

C)

D)

...

Question 3

Represent the following with a graph.
-
A)

B)

C)

D)

Accepted Answer

The answer of Represent the following with a graph.
-
A)

B)

C)

D)

...

Question 4

Determine whether the graph is a complete graph.
-
A) $\mathrm { No }$
B) Yes

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 5

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?

Accepted Answer

The answer of Solve the problem.
-Six freshmen move into a...

Question 6

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

Accepted Answer

Each member of the baseball team shakes hands with each member of the opposing team. If there are 9 members on each team, then each member of one team shakes hands with 9 members of the other team, resulting in 9 x 9 = 81 handshakes.

Question 7

Determine whether the graph is a complete graph.
-
A) $\mathrm { No }$
B) Yes

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 8

Determine whether the graph is a complete graph.
-
A) Yes
B) No

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 9

Determine whether the graph is a complete graph.
-
A) No
B) Yes

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 10

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?

Accepted Answer

The answer of Solve the problem.
-A computer network is to...

Question 11

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?

Accepted Answer

The answer of Solve the problem.
-Two schools play a tennis...

Question 12

Represent the following with a graph.
- 
A)

B)

C)

D)

Accepted Answer

The answer of Represent the following with a graph.
- 
A)

B)

C)

D)
...

Question 13

Determine whether the graph is a complete graph.
-
A) $Yes$
B) $\mathrm { No }$

Accepted Answer

The answer of Determine whether the graph is a complete...

Question 14

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.

Accepted Answer

The answer of James, Carl, Mark, Antonio, Phillip, and Brad...

Question 15

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.

Accepted Answer

The answer of James, Carl, Mark, Antonio, Phillip, and Brad...

Question 16

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. 
A)

B)

C)

D)

Accepted Answer

The answer of Represent the following with a graph.
-Create a...

Question 17

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

Accepted Answer

The answer of Seven family members are planning a picnic....

Question 18

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?

Accepted Answer

The answer of Solve the problem.
-A psychology class decides to...

Question 19

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?

Accepted Answer

The answer of Solve the problem.
-An internet user is participating...

Question 20

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

Accepted Answer

The total number of different patrol pairs can be calculated by adding the number of unique partners each officer has and dividing by 2 (since each pair is counted twice in this sum). The calculation is as follows: (2 officers * 5 partners + 4 officers * 3 partners + 2 officers * 2 partners + 2 officers * 1 partner) / 2 = (10 + 12 + 4 + 2) / 2 = 28 / 2 = 14.

Quiz 15: Graph Theory

Determine whether the graph is a complete graph. - $Determine whether the graph is a complete graph. - A) \mathrm { No } B) Yes$

Represent the following with a graph. -

Represent the following with a graph. -

Determine whether the graph is a complete graph. - $Determine whether the graph is a complete graph. - A) \mathrm { No } B) Yes$

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?

Determine whether the graph is a complete graph. - $Determine whether the graph is a complete graph. - A) \mathrm { No } B) Yes$

Determine whether the graph is a complete graph. -

Determine whether the graph is a complete graph. -

Represent the following with a graph. -

Determine whether the graph is a complete graph. - $Determine whether the graph is a complete graph. - A) Yes B) \mathrm { No }$

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.

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?

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?

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?