Does the graph of the bridges to the parts of the city create an Euler circuit, an Euler path, or neither. Explain how you know. If the tour guide wants to end where he started so people can get back in their cars, then how many bridges will he have to reuse? Explain. Hint: Make it an Euler Circuit.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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  1. Does the graph of the bridges to the parts of the city create an Euler circuit, an Euler path, or neither. Explain how you know.





  1. If the tour guide wants to end where he started so people can get back in their cars, then how many bridges will he have to reuse? Explain. Hint: Make it an Euler Circuit.






  1. Give the tour guide a sample plan where the group can see every bridge and end where they started.







  1. If the tour guide wants to just see every bridge and he ends in a different place than where the tour began, then how many bridges will he have to reuse? Explain. Hint: Make it an Euler Path







5. Give the tour guide a sample plan where the group can see every bridge and he ends in a different place than where the tour began.

Graph Theory: Königsberg Bridge Activity
Here is a picture of the city, Königsberg. As you can see, the city has multiple rivers
flowing through the city that requires the residents to build multiple bridges to get from one part
of the city to the other. There are currently 7 bridges connecting certain parts of the city to
another. A tour guide is looking at taking a group of people on a bus tour across the city to show
them all the bridges. The tour guide wants to come up with a plan that has him crossing the
bridges in the city as few times as possible while still planning on going over all the bridges. He
has asked for your help in planning the tour. Use your knowledge of Graph Theory to help the
tour guide to plan the route for the bus tour.
Transcribed Image Text:Graph Theory: Königsberg Bridge Activity Here is a picture of the city, Königsberg. As you can see, the city has multiple rivers flowing through the city that requires the residents to build multiple bridges to get from one part of the city to the other. There are currently 7 bridges connecting certain parts of the city to another. A tour guide is looking at taking a group of people on a bus tour across the city to show them all the bridges. The tour guide wants to come up with a plan that has him crossing the bridges in the city as few times as possible while still planning on going over all the bridges. He has asked for your help in planning the tour. Use your knowledge of Graph Theory to help the tour guide to plan the route for the bus tour.
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