The book "Fundamentals of Domination in Graphs" by Teresa W. Haynes, Stephen T. Hedetniemi, and Peter J. Slater provides a comprehensive treatment of the theory and applications of domination in graphs. The authors aim to present a self-contained, detailed exploration of the subject, covering both theoretical and algorithmic aspects. The book is suitable for graduate-level courses in graph theory, advanced undergraduate courses, and as a reference for researchers and students in various fields such as mathematics, computer science, operations research, and engineering. The book begins with an introduction to graph theory, defining key concepts such as vertices, edges, neighborhoods, degrees, paths, cycles, and matrices. It then delves into the core topics of domination, including dominating sets, dominating functions, and frameworks for domination. The authors discuss the complexity of domination problems and present algorithms for solving them. The book also includes a bibliography of over 300 authors, making it a valuable resource for researchers and students. The authors emphasize the importance of local subset problems, where solutions are found by examining closed neighborhoods independently. They illustrate this with examples from facility location and scheduling problems, such as the p-center problem and the p-median problem. The book concludes with exercises and a detailed bibliography, making it a comprehensive reference for further study. Overall, the book is a significant contribution to the field of graph theory, providing a thorough and accessible treatment of domination in graphs.The book "Fundamentals of Domination in Graphs" by Teresa W. Haynes, Stephen T. Hedetniemi, and Peter J. Slater provides a comprehensive treatment of the theory and applications of domination in graphs. The authors aim to present a self-contained, detailed exploration of the subject, covering both theoretical and algorithmic aspects. The book is suitable for graduate-level courses in graph theory, advanced undergraduate courses, and as a reference for researchers and students in various fields such as mathematics, computer science, operations research, and engineering. The book begins with an introduction to graph theory, defining key concepts such as vertices, edges, neighborhoods, degrees, paths, cycles, and matrices. It then delves into the core topics of domination, including dominating sets, dominating functions, and frameworks for domination. The authors discuss the complexity of domination problems and present algorithms for solving them. The book also includes a bibliography of over 300 authors, making it a valuable resource for researchers and students. The authors emphasize the importance of local subset problems, where solutions are found by examining closed neighborhoods independently. They illustrate this with examples from facility location and scheduling problems, such as the p-center problem and the p-median problem. The book concludes with exercises and a detailed bibliography, making it a comprehensive reference for further study. Overall, the book is a significant contribution to the field of graph theory, providing a thorough and accessible treatment of domination in graphs.