A-42 ANSWERS 25. a) T N A S Q P J 26. a) P U I Sw G A C SI 27. a) V M L T C 28. a) B Z U A C P 29. a) A B D F E C O 30. a) A B C D O E 31. a) A O C D B E 32. a) A C D B O E 55. b) California, Nevada, and Louisiana (and others) have an odd number of states bordering them. Since a graph of the United States would have more than two odd vertices, no Euler path and no Euler circuit exist. 57. a) A b) A B c) A B SECTION 13.3, PAGE 873 7. O 39 63 72 39 44 67 H M K 8. 92 44 62 37 117 101 94 71 76 45 D C B N T 35. K O B F GR L D 36. MB GB D LR B G K/D O 37. GB GR FB K L B SB E DR G O 38. GB FB SB B LR G MB D H DR K RR O 39. C A F E G B D 40. I J A C B E F G H D K 43. d) The sum of the degrees is equal to twice the number of edges, which is true, since each edge must connect two vertices. Each edge then contributes two to the sum of the degrees. 44. B D K M Other answers are possible L J SECTION 13.2, PAGE 861 23. a) OR WA ID MT WY 24. a) GA FL SC TX LA MS AL
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