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Chapter 14: Problem 55
What are equivalent graphs?
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Group members should determine a project whose installation would enhance the quality of life on campus or in your community. For example, the project might involve installing awnings over campus sidewalks, building a community bike path, creating a community hiking trail, or installing a metrorail system providing easy access to your community's most desirable locations. The project that you determine should be one that can be carried out most efficiently using a minimum spanning tree. Begin by defining the project and its locations (vertices). Group members should then research the distances between the various locations in the project. Once these distances have been determined, the group should reassemble and create a graph that models the project. Then find a minimum spanning tree that serves as the most efficient way to carry out your project.
What is a bridge?
Use a tree to model the employee relationships among the chief administrators of a large community college system: Three campus vice presidents report directly to the college president. On two campuses, the academic dean, the dean for administration, and the dean of student services report directly to the vice president. On the third campus, only the academic dean and the dean for administration report directly to the vice president.
In Exercises 11-16, a graph with no loops or more than one edge between any two vertices is described. Which one of the following applies to the description? i. The described graph is a tree. ii. The described graph is not a tree. iii. The described graph may or may not be a tree. The graph has five vertices and four edges.
An efficient solution for solving traveling salesperson problems has eluded mathematicians for more than 50 years. What explanations can you offer for this?
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