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. - Offers practical instruction in graph theory applications, graph coloring, network flows, graph invariants, graph cryptography, graph machine learning, graph minors, and random graph theory, among other topics - Exercises and open research questions encourage independent problem-solving and critical thinking skills - Features key term definitions, proofs and algorithms, summary points, exercises and solutions, and open problems for discussion across each chapter - Includes additional exercises, solutions, examples, and case studies in graph theory applications on supporting student and instructor sites
