Question 1

Decide if an Euler circuit exists for the graph.
-

Accepted Answer

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

Question 2

Represent the following with a graph.
-

Accepted Answer

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

Question 3

Determine whether the graph is a complete graph.
-

Accepted Answer

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

Question 4

Determine whether the sequence of vertices is an Euler circuit.
- 
$C \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow C$

Accepted Answer

A)  $Y e s$ 
B)  $\mathrm { No }$ 
A)  $Y e s$ 
B)  $\mathrm { No }$

Question 5

Decide if an Euler circuit exists for the graph.
-

Accepted Answer

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

Question 6

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.

Accepted Answer

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

Question 7

Determine whether the sequence of vertices is an Euler circuit.
- 
$A \rightarrow B \rightarrow C \rightarrow A \rightarrow E \rightarrow C \rightarrow D \rightarrow E \rightarrow F$

Accepted Answer

A)  No 
B)  $Y e s$ 
A)  No 
B)  $Y e s$

Question 8

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism.
-(a)

(b)

Accepted Answer

(a)
@#IMG-DLM&

(b)
@#IMG-DLM&

No. In g

Question 9

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

$\mathrm { I } \rightarrow \mathrm { L } \rightarrow \mathrm { K } \rightarrow \mathrm { H } \rightarrow \mathrm { I }$

Accepted Answer

A)  None of these 
B)  Walk and path 
C)  Walk, path, and circuit 
D)  Walk only 
A)  None of these 
B)  Walk and path 
C)  Walk, path, and circuit 
D)  Walk only

Question 10

Determine how many vertices and how many edges the graph has.
-

Accepted Answer

A)  6 vertices; 7 edges 
B)  5 vertices; 8 edges 
C)  5 vertices; 6 edges 
D)  5 vertices; 7 edges 
A)  6 vertices; 7 edges 
B)  5 vertices; 8 edges 
C)  5 vertices; 6 edges 
D)  5 vertices; 7 edges

Question 11

Identify the cut edges in the graph or say there are none.
-

Accepted Answer

A)  CF and DG 
B)  None 
C)  $\mathrm { DH }$ 
D)  $C D$ 
A)  CF and DG 
B)  None 
C)  $\mathrm { DH }$ 
D)  $C D$

Question 12

Determine how many vertices and how many edges the graph has.
-

Accepted Answer

A)  6 vertices; 5 edges 
B)  6 vertices; 1 edge 
C)  6 vertices; 3 edges 
D)  6 vertices; 6 edges 
A)  6 vertices; 5 edges 
B)  6 vertices; 1 edge 
C)  6 vertices; 3 edges 
D)  6 vertices; 6 edges

Question 13

Decide if an Euler circuit exists for the graph.
-

Accepted Answer

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

Question 14

Decide if an Euler circuit exists for the graph.
-

Accepted Answer

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

Question 15

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.

Accepted Answer

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

Question 16

Represent the following with a graph.
-

Accepted Answer

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

Question 17

Decide if an Euler circuit exists for the graph.
-

Accepted Answer

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

Question 18

Determine how many vertices and how many edges the graph has.
-

Accepted Answer

A)  5 vertices; 8 edges 
B)  7 vertices; 5 edges 
C)  5 vertices; 7 edges 
D)  5 vertices; 5 edges 
A)  5 vertices; 8 edges 
B)  7 vertices; 5 edges 
C)  5 vertices; 7 edges 
D)  5 vertices; 5 edges

Question 19

Determine how many components the graph has.
-

Accepted Answer

A)  1 
B)  5 
C)  3 
D)  7 
A)  1 
B)  5 
C)  3 
D)  7

Question 20

Identify the cut edges in the graph or say there are none.
-

Accepted Answer

A)  $\mathrm{DE}, \mathrm{EF} \text {, and } \mathrm{DF}$ 
B)   $\mathrm{BD}, \mathrm{CE}, \text { and } \mathrm{FI}$ 
C)  $\text { None }$ 
D)  $\mathrm{AB}, \mathrm{AC}, \mathrm{CH}, \mathrm{BG}, \mathrm{GI} \text {, and HI }$ 
A)  $\mathrm{DE}, \mathrm{EF} \text {, and } \mathrm{DF}$ 
B)   $\mathrm{BD}, \mathrm{CE}, \text { and } \mathrm{FI}$ 
C)  $\text { None }$ 
D)  $\mathrm{AB}, \mathrm{AC}, \mathrm{CH}, \mathrm{BG}, \mathrm{GI} \text {, and HI }$

Decide if an Euler circuit exists for the graph. -

Represent the following with a graph. -

Determine whether the graph is a complete graph. -

Determine whether the sequence of vertices is an Euler circuit. - $Determine whether the sequence of vertices is an Euler circuit. - C \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow C$ $C \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow C$

Decide if an Euler circuit exists for the graph. -

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.

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism. -(a) (b)

Determine how many vertices and how many edges the graph has. -

Identify the cut edges in the graph or say there are none. -

Determine how many vertices and how many edges the graph has. -

Decide if an Euler circuit exists for the graph. -

Decide if an Euler circuit exists for the graph. -

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.

Represent the following with a graph. -

Decide if an Euler circuit exists for the graph. -

Determine how many vertices and how many edges the graph has. -

Determine how many components the graph has. -

Identify the cut edges in the graph or say there are none. -

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Voting and Apportionment

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Exam 15: Graph Theory

Decide if an Euler circuit exists for the graph. -

Represent the following with a graph. -

Determine whether the graph is a complete graph. -

Determine whether the sequence of vertices is an Euler circuit. - C→D→E→A→B→CC \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow CC→D→E→A→B→C

Decide if an Euler circuit exists for the graph. -

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.

Determine whether the sequence of vertices is an Euler circuit. - A→B→C→A→E→C→D→E→FA \rightarrow B \rightarrow C \rightarrow A \rightarrow E \rightarrow C \rightarrow D \rightarrow E \rightarrow FA→B→C→A→E→C→D→E→F

Determine whether the two graphs are isomorphic. If they are, illustrate the isomorphism. -(a) (b)

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph. - I→L→K→H→I\mathrm { I } \rightarrow \mathrm { L } \rightarrow \mathrm { K } \rightarrow \mathrm { H } \rightarrow \mathrm { I }I→L→K→H→I

Determine how many vertices and how many edges the graph has. -

Identify the cut edges in the graph or say there are none. -

Determine how many vertices and how many edges the graph has. -

Decide if an Euler circuit exists for the graph. -

Decide if an Euler circuit exists for the graph. -

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.

Represent the following with a graph. -

Decide if an Euler circuit exists for the graph. -

Determine how many vertices and how many edges the graph has. -

Determine how many components the graph has. -

Identify the cut edges in the graph or say there are none. -

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Voting and Apportionment

Filters

Determine whether the sequence of vertices is an Euler circuit. - $Determine whether the sequence of vertices is an Euler circuit. - C \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow C$ $C \rightarrow D \rightarrow E \rightarrow A \rightarrow B \rightarrow C$