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haynes t domination graphs core concepts 2023

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Textbook in PDF format This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. With the enormous literature that exists on domination in graphs and the dynamic nature of the subject, we were faced with the challenge of determining which topics to include and perhaps even more importantly which topics to exclude, even for the core concepts of domination, total domination, and independent domination. We have therefore been selective in the material included in this core domination book and wish to apologize in advance for omitting many important results and proofs due to space limitations. We assume that the reader is acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. However, since graph theory terminology sometimes varies, we provide a glossary as a reference source for the reader regarding terminology and notation adopted in this book. Assuming that the reader has some familiarity with graph theory, this book is self-contained as we include the terminology and definitions involving domination in the glossary in Appendix A. The material in this book has been organized into 18 chapters, an epilogue, and three appendices. It contains an extensive bibliography of more than 900 references, which we have cited throughout the book

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haynes t domination graphs core concepts 2023