862 CHAPTER 13 Graph Theory 21. Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Water Island Island Land Land a) Yes b) They could start on either island and finish at the other. 22. Bridge Bridge Bridge Bridge Bridge Bridge Bridge Bridge Water Island Island Land Land a) Yes b) They could start either on the land at the top of the artwork or on the island on the left. If they started on the island, they would end on the land at the top, and vice versa. Vacations In Exercises 23 and 24, the maps of states that the Jugo family (see Example 4) is planning to visit on future vacations are shown. Use these graphs to complete the exercises. 23. Northwestern states Washington (WA) Oregon (OR) Idaho (ID) Montana (MT) Wyoming (WY) a) Represent the map as a graph. Use the state abbreviations to label the vertices of the graph. * b) Determine (state yes or no) whether the graph in part (a) has an Euler circuit. If yes, give one such Euler circuit. Yes; WA ID MT WY ID OR WA , , , , , , 24. Southeastern states Texas (TX) Louisiana (LA) Florida (FL) Mississippi (MS) Alabama (AL) Georgia (GA) South Carolina (SC) a) Represent the map as a graph. Use the state abbreviations to label the vertices of the graph. * b) Determine (state yes or no) whether the graph in part (a) has an Euler path or an Euler circuit. If yes, give one such Euler path or circuit. No Areas of the World In Exercises 25–28, use each map shown. a) Represent the map as a graph. Use the letter indicated in parentheses to label vertices of the graph. b) Determine (state yes or no) whether the graph in part (a) has an Euler path. If yes, give one such Euler path. c) Determine (state yes or no) whether the graph in part (a) has an Euler circuit. If yes, give one such Euler circuit. 25. Southwest Asia Afghanistan A( ), Iran N( ), Iraq Q( ), Jordan J( ), Pakistan P( ), Syria S( ), and Turkiye T( ). a) * b) Yes; STNAPNQJSQT , , , , , , , , , , c) No Pakistan Afghanistan Iran Iraq Syria Jordan Turkiye 26. Central Europe Austria A( ), Czech Republic C( ), Germany G( ), Italy I( ), Poland P( ), Slovakia, SL ( ), Switzerland SW ( ), and Ukraine U( ) a) * b) Yes; SWIASWGACGPCSLPUSLA , , , ,,,,,,, ,, , , c)No Switzerland Poland Germany Italy Austria Czech Republic Slovakia Ukraine *See Instructor Answer Appendix
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