Exam 15: Graph Theory

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, one of degree 4, three of degree 2, and four of degree 1.

(Multiple Choice)

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Question 61

Ten police officers patrol in pairs. Two officers have each patrolled with 5 other officers, four officers have patrolled with 3 others, two have patrolled with 2 others, and two have patrolled with Only 1 other officer. How many different patrol pairs have there been?

(Multiple Choice)

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Question 62

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 63

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 64

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

(Multiple Choice)

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Question 65

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 66

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

(Multiple Choice)

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Question 67

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 4 vertices each of degree 2.

(Multiple Choice)

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Question 68

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 69

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, two of degree 2, three of degree 1, and one of degree 3.

(Multiple Choice)

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Question 70

Determine how many components the graph has. -

(Multiple Choice)

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Question 71

Decide if an Euler circuit exists for the graph. -

(Multiple Choice)

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Question 72

Represent the following with a graph. -

(Multiple Choice)

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Question 73

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

(Multiple Choice)

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Question 74

Decide if an Euler circuit exists for the graph. -

(Multiple Choice)

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Question 75

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

(Multiple Choice)

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Question 76

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

(Multiple Choice)

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Question 77

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

(Essay)

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Question 78

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

(Multiple Choice)

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Question 79

Determine whether the graph is a complete graph. -

(Multiple Choice)

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Question 80

Showing 61 - 80 of 110

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, one of degree 4, three of degree 2, and four of degree 1.

Ten police officers patrol in pairs. Two officers have each patrolled with 5 other officers, four officers have patrolled with 3 others, two have patrolled with 2 others, and two have patrolled with Only 1 other officer. How many different patrol pairs have there been?

Determine whether the graph is connected or disconnected. -

Determine whether the graph is connected or disconnected. -

Determine whether the graph is connected or disconnected. -

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

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 4 vertices each of degree 2.

Determine whether the graph is connected or disconnected. -

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, two of degree 2, three of degree 1, and one of degree 3.

Determine how many components the graph has. -

Decide if an Euler circuit exists for the graph. -

Represent the following with a graph. -

Decide if an Euler circuit exists for the graph. -

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

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

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. -

Determine whether the graph is a complete 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

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Exam 15: Graph Theory

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, one of degree 4, three of degree 2, and four of degree 1.

Ten police officers patrol in pairs. Two officers have each patrolled with 5 other officers, four officers have patrolled with 3 others, two have patrolled with 2 others, and two have patrolled with Only 1 other officer. How many different patrol pairs have there been?

Determine whether the graph is connected or disconnected. -

Determine whether the graph is connected or disconnected. -

Determine whether the graph is connected or disconnected. -

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

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 4 vertices each of degree 2.

Determine whether the graph is connected or disconnected. -

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, two of degree 2, three of degree 1, and one of degree 3.

Determine how many components the graph has. -

Decide if an Euler circuit exists for the graph. -

Represent the following with a graph. -

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

Decide if an Euler circuit exists for the graph. -

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

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

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. -

Determine whether the graph is a complete 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

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

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