Question 1

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

Accepted Answer

A)   Euler path: A, B, C, D, E, F, G, H, C, A, H
B)   Euler circuit: A, B, C, D, E, F, G, H, A
C)   Euler path: A, B, C, D, E, F, G, H, A
D)   neither D

Question 2

$$\text { Determine whether or not the graph is a tree. If it is not, explain why. }$$

Accepted Answer

A)   The graph is not a tree because two edges overlap.
B)   The graph is not a tree because it is disconnected.
C)   The graph is not a tree because it contains a circuit.
D)   The graph is a tree.  B

Question 3

$$\text { List the odd vertices of the graph. }$$

Accepted Answer

A)   B, C
B)   A, B, C, D, E, F
C)   A, D, E, F
D)   A, D  C

Question 4

$$\text { List the edges that are bridges. }$$

Accepted Answer

A)   AE, BC, DF
B)   A, D
C)   AE, DF
D)   E, F

Question 5

Draw a graph that represents the floor plan. Use vertices to represent the rooms and outside area and edges to represent the connecting doors. Determine if the graph has an Euler path, and Euler circuit, or neither. If the graph has an Euler path or an Euler circuit. find one.

A)

neither

B)

neither

C)

Euler circuit: P-M-S-O-R-M-P

D)

Euler path P-M-S-O-R-M

Accepted Answer

The answer of Draw a graph that represents the floor...

Question 6

Determine if an Euler path or an Euler circuit exists so that a person who plows the roads does not have to pass over any street twice. If an Euler path or an Euler circuit exists, find one. The intersections of the streets have been labeled for you.

Accepted Answer

A)   Euler path: C-B-A-H-G-I-J-F-E-D-C-F
B)   Euler circuit: B-A-H-G-B-C-D-E-F-G-I-J-F-C-B
C)   Euler path: B-A-H-G-B-C-D-E-F-G-I-J-F-C
D)   neither exists

Question 7

$$\text { List the vertices of the graph. }$$

Accepted Answer

A)   A, F
B)   A, B, C, D
C)   B, C, D, E
D)   A, B, C, D, E, F

Question 8

Decide whether the connected graph has an Euler path, an Euler circuit, an Euler circuit butnot an Euler path, or neither an Euler circuit nor an Euler path. The graph has 4 odd vertices and 5 even vertices.

Accepted Answer

A)   Euler circuit
B)   Euler circuit but not an Euler path
C)   neither an Euler circuit nor an Euler path
D)   Euler path

Question 9

Draw a graph for the figure using vertices for the islands and edges for the bridges. Determine if the graph has an Euler path, an Euler circuit, or neither. If it has an Euler 
path or Euler circuit, find one.

A)

Euler path: A-D-C-B-A-C neither

B)

C)

Euler circuit: D-C-B-A-D

D)

Euler path: D-A-B-C-D-B

Accepted Answer

The answer of Draw a graph for the figure using...

Question 10

At a concert, the production manager needs to run electricity to several lights. The distances in feet are shown. Use a minimum spanning tree to determine the shortest amount of wire that will be needed.

Accepted Answer

A)   172 feet
B)   176 feet
C)   181 feet
D)   192 feet

Question 11

Draw a graph that represents the floor plan. Use vertices to represent the rooms and outside area and edges to represent the connecting doors.

A)

B)

C)

D)

Accepted Answer

The answer of Draw a graph that represents the floor...

Question 12

Based on the information in the table, use the brute force method to find the shortest routefrom Angleton to all the other cities and back to Angleton.

$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Distance (in miles) between Cities }$
$\begin{array}{l|cccc} 
& \text { Angleton } & \text { Benton } & \text { Coppell } & \text { Doran } \
\hline \text { Angleton } & - & 60 & 66 & 61 \
\text { Benton } & 60 & - & 48 & 74 \
\text { Coppell } & 66 & 48 & - & 55 \
\text { Doran } & 61 & 74 & 55 & -
\end{array}$

Accepted Answer

A)   255 miles
B)   249 miles
C)   215 miles
D)   224 miles

Question 13

Based on the information in the table, use the nearest neighbor method to find an approximation to the shortest route from Angleton to all the other cities and back to Angleton.

$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Distance (in miles) between Cities }$
$\begin{array}{l|cccc} 
& \text { Angleton } & \text { Benton } & \text { Coppell } & \text { Doran } \
\hline \text { Angleton } & - & 60 & 69 & 65 \
\text { Benton } & 60 & - & 50 & 74 \
\text { Coppell } & 69 & 50 & - & 52 \
\text { Doran } & 65 & 74 & 52 & -
\end{array}$

Accepted Answer

A)   243 miles
B)   227 miles
C)   255 miles
D)   258 miles

Question 14

$\text { Find a Hamiltonian circuit. }$

Accepted Answer

A)   F, D, C, B, A, E, D, F
B)   E, B, A, D, F, C, E
C)   A, E, B, C, F, D, E, A
D)   F, D, E, A, B, C, F

Question 15

Represent the figure using a graph. Use vertices for islands and edges for bridges.

A)

B)

C)

D)

Accepted Answer

The answer of Represent the figure using a graph. Use...

Question 16

$$\text { Find a Hamiltonian path. }$$

Accepted Answer

A)   F, D, C, B, A, E
B)   D, E, A, B, C, D, F
C)   F, D, A, B, C, E
D)   E, A, D, C, B, A, D, F

Question 17

$$\text { Use the brute force method to find the optimal solution for the weighted graph. }$$

Accepted Answer

A)   246
B)   209
C)   221
D)   249

Question 18

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

Accepted Answer

A)   neither
B)   Euler circuit: A, B, C, D, E, F, D, G, H, C, A
C)   Euler path: H, C, A, B, C, D, E, F, D, G
D)   Euler path: H, C, A, B, C, D, E, F, D, G, H, G

Question 19

Find the number of Hamilton circuits if a complete graph has five vertices.

Accepted Answer

A)   24
B)   32
C)   720
D)   120

Question 20

$$\text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. }$$

Accepted Answer

A)   304
B)   238
C)   213
D)   303

Exam 14: Available Online: Other Mathematical Systems

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

$\text { List the odd vertices of the graph. }$ $\text { List the odd vertices of the graph. } A) B, C B) A, B, C, D, E, F C) A, D, E, F D) A, D$

$\text { List the edges that are bridges. }$ $\text { List the edges that are bridges. } A) AE, BC, DF B) A, D C) AE, DF D) E, F$

Determine if an Euler path or an Euler circuit exists so that a person who plows the roads does not have to pass over any street twice. If an Euler path or an Euler circuit exists, find one. The intersections of the streets have been labeled for you.

$\text { List the vertices of the graph. }$ $\text { List the vertices of the graph. } A) A, F B) A, B, C, D C) B, C, D, E D) A, B, C, D, E, F$

Decide whether the connected graph has an Euler path, an Euler circuit, an Euler circuit butnot an Euler path, or neither an Euler circuit nor an Euler path. The graph has 4 odd vertices and 5 even vertices.

At a concert, the production manager needs to run electricity to several lights. The distances in feet are shown. Use a minimum spanning tree to determine the shortest amount of wire that will be needed.

Draw a graph that represents the floor plan. Use vertices to represent the rooms and outside area and edges to represent the connecting doors. A) B) C) D)

$\text { Find a Hamiltonian circuit. }$ $\text { Find a Hamiltonian circuit. } A) F, D, C, B, A, E, D, F B) E, B, A, D, F, C, E C) A, E, B, C, F, D, E, A D) F, D, E, A, B, C, F$

Represent the figure using a graph. Use vertices for islands and edges for bridges. A) B) C) D)

$\text { Find a Hamiltonian path. }$ $\text { Find a Hamiltonian path. } A) F, D, C, B, A, E B) D, E, A, B, C, D, F C) F, D, A, B, C, E D) E, A, D, C, B, A, D, F$

$\text { Use the brute force method to find the optimal solution for the weighted graph. }$ $\text { Use the brute force method to find the optimal solution for the weighted graph. } A) 246 B) 209 C) 221 D) 249$

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

Find the number of Hamilton circuits if a complete graph has five vertices.

$\text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. }$ $\text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. } A) 304 B) 238 C) 213 D) 303$

Exam 14: Available Online: Other Mathematical Systems

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

Determine whether or not the graph is a tree. If it is not, explain why. \text { Determine whether or not the graph is a tree. If it is not, explain why. } Determine whether or not the graph is a tree. If it is not, explain why.

List the odd vertices of the graph. \text { List the odd vertices of the graph. } List the odd vertices of the graph.

List the edges that are bridges. \text { List the edges that are bridges. } List the edges that are bridges.

Determine if an Euler path or an Euler circuit exists so that a person who plows the roads does not have to pass over any street twice. If an Euler path or an Euler circuit exists, find one. The intersections of the streets have been labeled for you.

List the vertices of the graph. \text { List the vertices of the graph. } List the vertices of the graph.

Decide whether the connected graph has an Euler path, an Euler circuit, an Euler circuit butnot an Euler path, or neither an Euler circuit nor an Euler path. The graph has 4 odd vertices and 5 even vertices.

At a concert, the production manager needs to run electricity to several lights. The distances in feet are shown. Use a minimum spanning tree to determine the shortest amount of wire that will be needed.

Draw a graph that represents the floor plan. Use vertices to represent the rooms and outside area and edges to represent the connecting doors. A) B) C) D)

Find a Hamiltonian circuit. \text { Find a Hamiltonian circuit. } Find a Hamiltonian circuit.

Represent the figure using a graph. Use vertices for islands and edges for bridges. A) B) C) D)

Find a Hamiltonian path. \text { Find a Hamiltonian path. } Find a Hamiltonian path.

Use the brute force method to find the optimal solution for the weighted graph. \text { Use the brute force method to find the optimal solution for the weighted graph. } Use the brute force method to find the optimal solution for the weighted graph.

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an Euler circuit, find one.

Find the number of Hamilton circuits if a complete graph has five vertices.

Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. \text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. } Use the nearest neighbor method to approximate the optimal solution. Start at vertex A.

$\text { List the odd vertices of the graph. }$ $\text { List the odd vertices of the graph. } A) B, C B) A, B, C, D, E, F C) A, D, E, F D) A, D$

$\text { List the edges that are bridges. }$ $\text { List the edges that are bridges. } A) AE, BC, DF B) A, D C) AE, DF D) E, F$

$\text { List the vertices of the graph. }$ $\text { List the vertices of the graph. } A) A, F B) A, B, C, D C) B, C, D, E D) A, B, C, D, E, F$

$\text { Find a Hamiltonian circuit. }$ $\text { Find a Hamiltonian circuit. } A) F, D, C, B, A, E, D, F B) E, B, A, D, F, C, E C) A, E, B, C, F, D, E, A D) F, D, E, A, B, C, F$

$\text { Find a Hamiltonian path. }$ $\text { Find a Hamiltonian path. } A) F, D, C, B, A, E B) D, E, A, B, C, D, F C) F, D, A, B, C, E D) E, A, D, C, B, A, D, F$

$\text { Use the brute force method to find the optimal solution for the weighted graph. }$ $\text { Use the brute force method to find the optimal solution for the weighted graph. } A) 246 B) 209 C) 221 D) 249$

$\text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. }$ $\text { Use the nearest neighbor method to approximate the optimal solution. Start at vertex A. } A) 304 B) 238 C) 213 D) 303$