13.1 Graphs, Paths, and Circuits 851 30. Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Water Island Island Land Land * Vacations In Exercises 31 and 32, the maps of states that the Jugo family (see Example 2) is planning to visit on future vacations are shown. Represent each map as a graph where each vertex represents a state and each edge represents a common border between the states. Use the state abbreviations to label the vertices of the graph. 31. Northwestern states * Washington (WA) Oregon (OR) Idaho (ID) Montana (MT) Wyoming (WY) 32. Southeastern states * Texas (TX) Louisiana (LA) Florida (FL) Mississippi (MS) Alabama (AL) Georgia (GA) South Carolina (SC) 33. Central America The following map shows the countries of Belize B( ), Costa Rica C( ), El Salvador E( ), Guatemala G( ), Honduras H( ), Nicaragua (N), and Panama P( ). Represent the map as a graph where each vertex represents a country and each edge represents a common border between the countries. Use the letters indicated in parentheses to label the vertices. * In Exercises 25–28, a connected graph is shown. For each graph, identify any (a) bridges and (b) loops. 25. A B C D E F G a) Edge BC b) Loop FF 26. A B E C F G D H I J a) Edge BE b) Loop EE 27. A C B D E a) Edge BC b) No loop 28. A C B D E a) No bridges b) Loop CC Problem Solving Modified Königsberg Bridge Problems In Exercises 29 and 30, suppose that the people of Königsberg decide to add several bridges to their city. Two such possibilities are shown. Create graphs that would represent the Königsberg bridge problem with these new bridges. 29. Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Water Island Island Land Land * *See Instructor Answer Appendix
RkJQdWJsaXNoZXIy NjM5ODQ=