Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. Preface - p. xv 8. Chapter 1: Basics of graph theory - p. 1 9. Chapter 2: Graph representation - p. 25 10. Chapter 3: Graph connectivity - p. 39 11. Chapter 4: Trees and forests - p. 59 12. Chapter 5: Planar graphs - p. 77 13. Chapter 6: Hamiltonian and Eulerian graphs - p. 87 14. Chapter 7: Graph coloring - p. 107 15. Chapter 8: Graph operations - p. 123 16. Chapter 9: Matching theory - p. 137 17. Chapter 10: Graph invariants and parameters - p. 153 18. Chapter 11: Algebraic graph theory - p. 165 19. Chapter 12: Graph traversals - p. 177 20. Chapter 13: Shortest path algorithms - p. 193 21. Chapter 14: Network flows - p. 205 22. Chapter 15: Topological graph theory - p. 213 23. Chapter 16: Ramsey theory and extremal graph theory - p. 223 24. Chapter 17: Graph minors and decompositions - p. 239 25. Chapter 18: Graph algorithms and complexity theory - p. 249 26. Chapter 19: Graph-based cryptographic techniques - p. 261 27. Chapter 20: Graph theory and machine learning - p. 271 28. Chapter 21: Random graphs and probabilistic methods - p. 281 29. References - p. 289 30. Index - p. 291
Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. Preface - p. xv 8. Chapter 1: Basics of graph theory - p. 1 9. Chapter 2: Graph representation - p. 25 10. Chapter 3: Graph connectivity - p. 39 11. Chapter 4: Trees and forests - p. 59 12. Chapter 5: Planar graphs - p. 77 13. Chapter 6: Hamiltonian and Eulerian graphs - p. 87 14. Chapter 7: Graph coloring - p. 107 15. Chapter 8: Graph operations - p. 123 16. Chapter 9: Matching theory - p. 137 17. Chapter 10: Graph invariants and parameters - p. 153 18. Chapter 11: Algebraic graph theory - p. 165 19. Chapter 12: Graph traversals - p. 177 20. Chapter 13: Shortest path algorithms - p. 193 21. Chapter 14: Network flows - p. 205 22. Chapter 15: Topological graph theory - p. 213 23. Chapter 16: Ramsey theory and extremal graph theory - p. 223 24. Chapter 17: Graph minors and decompositions - p. 239 25. Chapter 18: Graph algorithms and complexity theory - p. 249 26. Chapter 19: Graph-based cryptographic techniques - p. 261 27. Chapter 20: Graph theory and machine learning - p. 271 28. Chapter 21: Random graphs and probabilistic methods - p. 281 29. References - p. 289 30. Index - p. 291
