Exam 15: Graph Theory

James, Carl, Mark, Antonio, Phillip, and Brad are friends at college. James, Antonio and Phillip have calculus together. Brad and Carl have the same English composition class. Draw a graph with vertices representing students and edges representing the relation "take a common class". How many components does the graph have? Identify a subgraph that is a complete subgraph with three vertices.

(Essay)

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Question 41

Decide if an Euler circuit exists for the graph. -

(Multiple Choice)

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Question 42

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

(Multiple Choice)

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Question 43

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

(Multiple Choice)

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Question 44

Determine whether the graph is a complete graph. -

(Multiple Choice)

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Question 45

Determine how many components the graph has. -

(Multiple Choice)

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Question 46

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

(Multiple Choice)

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Question 47

Determine how many components the graph has. -

(Multiple Choice)

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Question 48

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 49

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 10 vertices, three of degree 5, three of degree 3, two of degree 2, and two of degree 1.

(Multiple Choice)

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Question 50

Represent the following with a graph. -Create a graph that models the bordering relationship among the states shown in the map. Use vertices to represent the states and edges to represent common borders.

(Multiple Choice)

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Question 51

Decide if an Euler circuit exists for the graph. -

(Multiple Choice)

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Question 52

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

(Multiple Choice)

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Question 53

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

(Essay)

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Question 54

Determine whether the graph is connected or disconnected. -

(Multiple Choice)

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Question 55

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

(Multiple Choice)

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Question 56

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 5 vertices, three of degree 2 and two of degree 3.

(Multiple Choice)

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Question 57

Determine whether the graph is a complete graph. -

(Multiple Choice)

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Question 58

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

(Multiple Choice)

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Question 59

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

(Multiple Choice)

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Question 60

Showing 41 - 60 of 110

Decide if an Euler circuit exists for the graph. -

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

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

Determine whether the graph is a complete graph. -

Determine how many components the graph has. -

Determine how many components the graph has. -

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 10 vertices, three of degree 5, three of degree 3, two of degree 2, and two of degree 1.

Represent the following with a graph. -Create a graph that models the bordering relationship among the states shown in the map. Use vertices to represent the states and edges to represent common borders.

Decide if an Euler circuit exists for the graph. -

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

Determine whether the graph is connected or disconnected. -

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 5 vertices, three of degree 2 and two of degree 3.

Determine whether the graph is a complete graph. -

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Exam 15: Graph Theory

Decide if an Euler circuit exists for the graph. -

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

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

Determine whether the graph is a complete graph. -

Determine how many components the graph has. -

Determine whether the sequence of vertices is i)a walk, ii)a path, iii)a circuit in the given graph. - B→G→C→B→FB \rightarrow G \rightarrow C \rightarrow B \rightarrow FB→G→C→B→F

Determine how many components the graph has. -

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 10 vertices, three of degree 5, three of degree 3, two of degree 2, and two of degree 1.

Represent the following with a graph. -Create a graph that models the bordering relationship among the states shown in the map. Use vertices to represent the states and edges to represent common borders.

Decide if an Euler circuit exists for the graph. -

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

Determine whether the graph is connected or disconnected. -

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 5 vertices, three of degree 2 and two of degree 3.

Determine whether the graph is a complete graph. -

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

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

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