Question 1

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

Accepted Answer

B

Question 2

$\text { Find a Hamiltonian circuit. }$

Accepted Answer

D

Question 3

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

C

Question 4

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

Accepted Answer

The answer of \[\text { Determine whether or not the...

Question 5

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

The answer of State whether the graph has an Euler...

Question 6

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

The answer of Based on the information in the table,...

Question 7

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

Accepted Answer

The answer of \[\text { Use the nearest neighbor method...

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 2 odd vertices and 2 even vertices.

Accepted Answer

A graph with exactly two odd vertices has an Euler path but not an Euler circuit.

Question 9

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 graph has an Euler path if and only if it has exactly two odd vertices. A graph has an Euler circuit if and only if it has no odd vertices.

Question 10

Use Kruskal's algorithm to find a minimum spanning tree for the graph below. Give the total weight for the graph.

A)

weight: 135

B)

weight: 140

C)

weight: 130

D)

weight: 139

Accepted Answer

The answer of Use Kruskal's algorithm to find a minimum...

Question 11

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

Accepted Answer

The answer of \[\text { List the odd vertices of...

Question 12

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 13

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

Accepted Answer

A complete graph with n vertices has (n-1)! Hamiltonian circuits. For 5 vertices, it is (5-1)! = 4! = 24.

Question 14

$$\text { How many edges does the graph have? }$$

Accepted Answer

The answer of \[\text { How many edges does the...

Question 15

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

Starting from Angleton, the nearest city is Benton (60 miles), then Coppell (50 miles), then Doran (52 miles), and finally back to Angleton (65 miles). Total distance = 60 + 50 + 52 + 65 = 227 miles.

Question 16

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

Accepted Answer

The answer of \[\text { Use the brute force method...

Question 17

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

Accepted Answer

The answer of \[\text { Determine whether or not the...

Question 18

$$\text { Find a circuit that includes vertex } \mathrm { C } \text {. }$$

Accepted Answer

The answer of \[\text { Find a circuit that includes...

Question 19

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 20

Edges may be removed from the graph that follows so that is becomes a spanning tree. Identify a set of edges that can be removed to accomplish this.

Accepted Answer

The answer of Edges may be removed from the graph...

Quiz 14: Available Online: Other Mathematical Systems

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

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.

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.

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

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 2 odd vertices and 2 even vertices.

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.

Use Kruskal's algorithm to find a minimum spanning tree for the graph below. Give the total weight for the graph. A) weight: 135 B) weight: 140 C) weight: 130 D) weight: 139

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

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

$\text { How many edges does the graph have? }$ $\text { How many edges does the graph have? } A) 4 B) 6 C) 7 D) 1$

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

$\text { Find a circuit that includes vertex } \mathrm { C } \text {. }$ $\text { Find a circuit that includes vertex } \mathrm { C } \text {. } A) C, D, A, B, C B) C, D, F, C C) C, D, A, B D) C, D, F, D, C$

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)

Edges may be removed from the graph that follows so that is becomes a spanning tree. Identify a set of edges that can be removed to accomplish this.

Quiz 14: Available Online: Other Mathematical Systems

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.

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

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.

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.

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.

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.

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 2 odd vertices and 2 even vertices.

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.

Use Kruskal's algorithm to find a minimum spanning tree for the graph below. Give the total weight for the graph. A) weight: 135 B) weight: 140 C) weight: 130 D) weight: 139

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

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

How many edges does the graph have? \text { How many edges does the graph have? } How many edges does the graph have?

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.

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.

Find a circuit that includes vertex C. \text { Find a circuit that includes vertex } \mathrm { C } \text {. } Find a circuit that includes vertex C.

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)

Edges may be removed from the graph that follows so that is becomes a spanning tree. Identify a set of edges that can be removed to accomplish this.

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

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

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

$\text { How many edges does the graph have? }$ $\text { How many edges does the graph have? } A) 4 B) 6 C) 7 D) 1$

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

$\text { Find a circuit that includes vertex } \mathrm { C } \text {. }$ $\text { Find a circuit that includes vertex } \mathrm { C } \text {. } A) C, D, A, B, C B) C, D, F, C C) C, D, A, B D) C, D, F, D, C$