Question 1

Determine how many components the graph has.
-

Accepted Answer

A)  3 
B)  1 
C)  5 
D)  2 
A)  3 
B)  1 
C)  5 
D)  2

Question 2

Determine whether the graph is a complete graph.
-

Accepted Answer

A)  $Yes$ 
B)  $\mathrm { No }$ 
A)  $Yes$ 
B)  $\mathrm { No }$

Question 3

Use Fleury's algorithm to find an Euler circuit for the graph beginning and ending at the indicated vertex. If no Euler
circuit exists, state this.
-Using the following graph, find an Euler circuit that begins and ends with vertex A.

Accepted Answer

A)  $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{E} \rightarrow \mathrm{A} \rightarrow \mathrm{B}$ 
B)  $\text { No Euler circuit exists. }$ 
C)  $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{B} \rightarrow \mathrm{E} \rightarrow \mathrm{A}$ 
D)  $A \rightarrow B \rightarrow C \rightarrow D \rightarrow B \rightarrow A$ 
A)  $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{E} \rightarrow \mathrm{A} \rightarrow \mathrm{B}$ 
B)  $\text { No Euler circuit exists. }$ 
C)  $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{B} \rightarrow \mathrm{E} \rightarrow \mathrm{A}$ 
D)  $A \rightarrow B \rightarrow C \rightarrow D \rightarrow B \rightarrow A$

Question 4

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

Accepted Answer

A)  $\mathrm { AE } , \mathrm { AB }$, and $\mathrm { AC }$ 
B)  None 
C)  BI, EI, and FH 
D)  $\mathrm { EI }$ and $\mathrm { FH }$ 
A)  $\mathrm { AE } , \mathrm { AB }$, and $\mathrm { AC }$ 
B)  None 
C)  BI, EI, and FH 
D)  $\mathrm { EI }$ and $\mathrm { FH }$

Question 5

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 6 and six of degree 1.

Accepted Answer

A) 6 edges 
B) 7 edges 
C) 14 edges 
D) 13 edges 
A) 6 edges 
B) 7 edges 
C) 14 edges 
D) 13 edges

Question 6

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph.
- 
$\mathrm { B } \rightarrow \mathrm { H } \rightarrow \mathrm { F } \rightarrow \mathrm { G }$

Accepted Answer

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

Question 7

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 graph (a) t

Question 8

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 9

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 8 vertices, two of degree 2, four of degree 3, and two of degree 1.

Accepted Answer

A) 9 edges 
B) 6 edges 
C) 3 edges 
D) 18 edges 
A) 9 edges 
B) 6 edges 
C) 3 edges 
D) 18 edges

Question 10

Represent the following with a graph.
-

Accepted Answer

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

Determine how many components the graph has. -

Determine whether the graph is a complete graph. -

Use Fleury's algorithm to find an Euler circuit for the graph beginning and ending at the indicated vertex. If no Euler circuit exists, state this. -Using the following graph, find an Euler circuit that begins and ends with vertex A.

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

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 6 and six of degree 1.

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

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 8 vertices, two of degree 2, four of degree 3, and two of degree 1.

Represent the following with a graph. -

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

Exam 15: Graph Theory