Question 1

Find a circuit that includes vertex D.

Accepted Answer

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

Question 2

Are the two graphs equivalent?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No B

Question 3

List the vertices of the graph.

Accepted Answer

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

Question 4

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

Question 5

Based on the airfare information in the table below, draw a complete weighted graph for the table.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

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

Question 7

Suppose you're trying to make a final exam schedule for six classes: anthropology 107 (A),
Economics 212 (E), information systems 194 (I), statistics 261 (S), history 201 (H), and geology 101
(G). The graph below shows which classes students have in common: these are connected by edges.
Use graph coloring to find the chromatic number.

Accepted Answer

A) 3 
B) 2 
C) 4 
D) 5 
A) 3 
B) 2 
C) 4 
D) 5

Question 8

Use the brute force method to find the optimal solution for the weighted graph.

Accepted Answer

A) 258 
B) 222 
C) 254 
D) 216 
A) 258 
B) 222 
C) 254 
D) 216

Question 9

Find a Hamiltonian path.

Accepted Answer

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

Question 10

Find a Hamiltonian circuit.

Accepted Answer

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

Question 11

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

A) GH and FG 
B) GH and HI 
C) EF and EH 
D) HI and FI 
A) GH and FG 
B) GH and HI 
C) EF and EH 
D) HI and FI

Question 12

Using graph coloring, find the smallest number of colors needed to color the map so that no regions
Sharing a common border are the same color

Accepted Answer

A) 5 colors 
B) 4 colors 
C) 2 colors 
D) 3 colors 
A) 5 colors 
B) 4 colors 
C) 2 colors 
D) 3 colors

Question 13

List the even vertices of the graph.

Accepted Answer

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

Question 14

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) 193 feet 
B) 173 feet 
C) 178 feet 
D) 182 feet 
A) 193 feet 
B) 173 feet 
C) 178 feet 
D) 182 feet

Question 15

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

Question 16

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

Question 17

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.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

How many edges does the graph have?

Accepted Answer

A) 2 
B) 7 
C) 6 
D) 5 
A) 2 
B) 7 
C) 6 
D) 5

Question 19

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

Accepted Answer

A) 219 miles 
B) 250 miles 
C) 255 miles 
D) 216 miles 
A) 219 miles 
B) 250 miles 
C) 255 miles 
D) 216 miles

Question 20

List the edges that are bridges.

Accepted Answer

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

Find a circuit that includes vertex D.

Are the two graphs equivalent?

List the vertices of the graph.

Determine whether or not the graph is a tree. If it is not, explain why.

Based on the airfare information in the table below, draw a complete weighted graph for the table.

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 brute force method to find the optimal solution for the weighted graph.

Find a Hamiltonian path.

Find a Hamiltonian circuit.

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.

Using graph coloring, find the smallest number of colors needed to color the map so that no regions Sharing a common border are the same color

List the even vertices of the graph.

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.

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 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.

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.

How many edges does the graph have?

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

List the edges that are bridges.

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Exam 13: Graph Theory

Find a circuit that includes vertex D.

Are the two graphs equivalent?

List the vertices of the graph.

Determine whether or not the graph is a tree. If it is not, explain why.

Based on the airfare information in the table below, draw a complete weighted graph for the table.

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 brute force method to find the optimal solution for the weighted graph.

Find a Hamiltonian path.

Find a Hamiltonian circuit.

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.

Using graph coloring, find the smallest number of colors needed to color the map so that no regions Sharing a common border are the same color

List the even vertices of the graph.

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.

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 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.

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.

How many edges does the graph have?

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

List the edges that are bridges.

Problem Solving

Sets

Logic

Numeration Systems

The Real Number System

Topics in Algebra

Consumer Mathematics

Measurement

Geometry

Probability and Counting Techniques

Statistics

Voting Methods

Available Online: Other Mathematical Systems

Filters