Explanation Given information: The graph is Definition used: Planar graph: A planar graph is a graph that can be drawn so that no edges intersect each other (except at vertices). Proof: Consider the graph with naming the vertices,

Mathematical Excursions (MindTap Course List)

4th Edition

ISBN: 9781305965584

Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg

Publisher: Cengage Learning

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Question

Chapter 5.3, Problem 4ES

To determine

To Prove:

The given graph is a planar by finding a planar drawing.

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Chapter 5.3, Problem 3ES

Chapter 5.3, Problem 5ES

Chapter 5 Solutions

Mathematical Excursions (MindTap Course List)

Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Prob. 4ES Ch. 5.1 - Determine (a) the number of edges in the graph,...

Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Explain why the following two graphs cannot be...Ch. 5.1 - Label the vertices of the second graph so that it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Transportation For the train routes given in...Ch. 5.1 - Transportation For the direct air flights given in...Ch. 5.1 - Pets The diagram below shows the arrangement of a...Ch. 5.1 - Transportation A subway map is shown below. Is it...Ch. 5.1 - Prob. 29ES Ch. 5.1 - Prob. 30ES Ch. 5.1 - Degrees of Separation In the graph below, an edge...Ch. 5.1 - Social Network In the graph below, an edge...Ch. 5.1 - Prob. 33ES Ch. 5.1 - Travel A map of South America is shown at the...Ch. 5.2 - Continue investigating Hamiltonian circuits in...Ch. 5.2 - Use the greedy algorithm and the weighted graph...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Transportation For the train routes given in...Ch. 5.2 - Transportation For the direct air flights given in...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Travel A company representative lives in...Ch. 5.2 - Travel A tourist is staying in Toronto, Canada,...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Nicole wants to tour Asia. She will start...Ch. 5.2 - Travel The prices for traveling between five...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Route Planning Brian needs to visit the pet store,...Ch. 5.2 - Route Planning A bike messenger needs to deliver...Ch. 5.2 - Scheduling A research company has a large...Ch. 5.2 - Computer Networks A small office wishes to network...Ch. 5.2 - Route Planning A security officer patrolling a...Ch. 5.2 - Route Planning A city engineer needs to inspect...Ch. 5.2 - Draw a connected graph with six vertices that has...Ch. 5.2 - Assign weights to the edges of the following...Ch. 5.3 - The tetrahedron in figure 5.20 consists of four...Ch. 5.3 - The following graph is the projection of one ofthe...Ch. 5.3 - Prob. 3EE Ch. 5.3 - Give a reason why the graph below Cannot be the...Ch. 5.3 - Prob. 1ES Ch. 5.3 - Prob. 2ES Ch. 5.3 - Prob. 3ES Ch. 5.3 - Prob. 4ES Ch. 5.3 - Prob. 5ES Ch. 5.3 - Prob. 6ES Ch. 5.3 - Prob. 7ES Ch. 5.3 - Prob. 8ES Ch. 5.3 - Prob. 9ES Ch. 5.3 - Prob. 10ES Ch. 5.3 - Prob. 11ES Ch. 5.3 - Prob. 12ES Ch. 5.3 - Show that the following graph contracts to K5.Ch. 5.3 - Show that the following graph contracts to the...Ch. 5.3 - Prob. 15ES Ch. 5.3 - Prob. 16ES Ch. 5.3 - Prob. 17ES Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Prob. 23ES Ch. 5.3 - Prob. 24ES Ch. 5.3 - Prob. 25ES Ch. 5.3 - Prob. 26ES Ch. 5.3 - Prob. 27ES Ch. 5.3 - Prob. 28ES Ch. 5.3 - Prob. 29ES Ch. 5.3 - Prob. 30ES Ch. 5.4 - A one-way road ends at a two-way street. The...Ch. 5.4 - A one-way road intersects a two-way road in a...Ch. 5.4 - A two-way road intersects another two-way road in...Ch. 5.4 - Prob. 1ES Ch. 5.4 - Prob. 2ES Ch. 5.4 - Prob. 3ES Ch. 5.4 - Prob. 4ES Ch. 5.4 - Prob. 5ES Ch. 5.4 - Prob. 6ES Ch. 5.4 - Prob. 7ES Ch. 5.4 - Prob. 8ES Ch. 5.4 - Prob. 9ES Ch. 5.4 - Prob. 10ES Ch. 5.4 - Prob. 11ES Ch. 5.4 - Prob. 12ES Ch. 5.4 - Prob. 13ES Ch. 5.4 - Prob. 14ES Ch. 5.4 - Prob. 15ES Ch. 5.4 - Prob. 16ES Ch. 5.4 - Prob. 17ES Ch. 5.4 - Prob. 18ES Ch. 5.4 - Prob. 19ES Ch. 5.4 - Prob. 20ES Ch. 5.4 - Prob. 21ES Ch. 5.4 - Prob. 22ES Ch. 5.4 - Scheduling Six different groups of children would...Ch. 5.4 - Scheduling Five different charity organizations...Ch. 5.4 - Scheduling Students in a film class have...Ch. 5.4 - Animal Housing A researcher has discovered six new...Ch. 5.4 - Prob. 27ES Ch. 5.4 - Prob. 28ES Ch. 5.4 - Prob. 29ES Ch. 5.4 - Prob. 30ES Ch. 5.4 - Scheduling Edge colorings, as explained in...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - Soccer In the table below, an X indicates teams...Ch. 5 - Each vertex in the graph at the left represents a...Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Architecture The floor plan of a sculpture gallery...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Efficient Route The distances, in miles, between...Ch. 5 - Computer Networking A small office needs to...Ch. 5 - Prob. 23RE Ch. 5 - Prob. 24RE Ch. 5 - Prob. 25RE Ch. 5 - Prob. 26RE Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Prob. 29RE Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - Prob. 33RE Ch. 5 - Prob. 34RE Ch. 5 - Scheduling A company has scheduled a retreat at a...Ch. 5 - Social Network Each vertex in the graph at the...Ch. 5 - Determine whether the following two graphs are...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Recreation The illustration below depicts bridges...Ch. 5 - a. What does Dirac's theorem state? Explain how it...Ch. 5 - Low-Cost Route The table below shows the cost of...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Prob. 8T Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Prob. 10T Ch. 5 - Prob. 11T Ch. 5 - A group of eight friends is planning a vacation in...

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To Prove: The given graph is a planar by finding a planar drawing.

Solution Summary: The author explains that a planar graph can be drawn so that no edges intersect each other (except at vertices).

To Prove: The given graph is a planar by finding a planar drawing.

Want to see the full answer?

Chapter 5 Solutions

To Prove:

The given graph is a planar by finding a planar drawing.