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From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course Front Cover......Page 1 Back Cover......Page 2 Preface......Page 7 Contents......Page 11 1.1 Deduction......Page 15 1.2 Induction......Page 23 1.3 Sets and Relations......Page 36 1.4 Functions......Page 46 Review Problems......Page 53 2. Basic Counting Principles......Page 56 2.1 Sequential Counting......Page 57 2.2 Case-by-Case Counting......Page 64 2.3 Selections......Page 69 2.4 Selections with Unlimited Repetition......Page 78 2.5 Binomial Coefficients......Page 87 2.6 Permutations of Nondistinct Objects......Page 95 Review Problems......Page 99 3.1 The Union of Overlapping Sets......Page 102 3.2 Counting Restricted Arrangements......Page 110 3.3 Distributions......Page 116 Review Problems......Page 123 4.1 Algorithms......Page 125 4.2 Asymptotic Analysis of Algorithms......Page 133 4.3 Enumerating Permutations and Combinations (Optional)......Page 138 Review Problems......Page 145 5.1 Graph Models......Page 148 5.2 Paths and Connectedness......Page 159 5.3 Circuits and Cycles......Page 164 5.4 Planar Graphs......Page 173 5.5 Graph Colorings......Page 178 Review Problems......Page 185 6.1 Breadth First Search......Page 187 6.2 Trees......Page 194 6.3 Tree Algorithms......Page 202 Review Problems......Page 212 7.1 Generating Function Models......Page 214 7.2 Calculating Coefficients......Page 221 7.3 Partitions......Page 227 7.4 Exponential Generating Functions......Page 233 Review Problems......Page 238 8.1 Recurrence Relation Models......Page 240 8.2 Homogeneous Linear Recurrences......Page 248 8.3 Nonhomogeneous Linear Recurrence Relations......Page 256 Review Problems......Page 264 9.1 Symmetry Groups and Burnside's Theorem......Page 267 9.2 The Cycle Index......Page 275 Review Problems......Page 282 10.1 Directed Graphs......Page 284 10.2 Networks......Page 292 10.3 Network Flows......Page 300 Hints and Answers to Odd-Numbered Problems......Page 313 Index......Page 331 Book by Jackson, Bradley, Thoro, Dmitri