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Discrete Mathematics and Its Applications Fifth Edition Kenneth H. Rosen AT&T Laboratories Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Franc~sco St. LOUIS Bangkok Bogota Caracas KuaIaLumpur Lisbon London Madrid MexicoC~ty Milan Montreal NewDelhi Santiago Seoul Singapore Sydney T a ~ p e ~ Toronto Contents v 8.7 Planar Graphs 8.8 Graph Coloring End-of-Chapter Material 9 Trees 631 Introduction to Trees Applications of Trees Tree Traversal Spanning Trces 9.5 Minimum Spanning
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  DiscreteMathematicsand Its Applications Fifth EditionKenneth H. Rosen AT&T Laboratories Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Franc~sco St. LOUISBangkok Bogota Caracas KuaIaLumpur Lisbon London Madrid MexicoC~tyMilan Montreal NewDelhi Santiago Seoul Singapore Sydney Ta~pe~ oronto  Contents v 8.7 Planar Graphs 8.8 Graph ColoringEnd-of-Chapter Material 9 Trees 631 0.1 Introduction to Trees 9.2 Applications of Trees 9.3 Tree Traversal 9.4 Spanning Trces 9.5 Minimum Spanning TreesEnd-of-Chapter Material 10 Boolean Algebra 701 10.1 Boolean Functions 10.2 Representing Boolean Functions10.3 Logic Gales 10.4 Minimization of CircuitsEnd-of-Chapter Material 11 Modeling Computation 739 11.1 Languages and Grammars 11.2 Finite-State Machines with Output 11.3 Finite-State Machines w~thNo Output11.4 Language Recognition 1 1.5 Turing MachinesEnd-of-Chapter Material Appendixes A.1 Exponential and Logarithmic Function\A.2 Pseudocode Suggested Readings B-1 Answers to Odd-Numbered Exercises S-1 Photo Credits C- l Index of Biographies 1-1 Index 1-2

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