Domination in graphs : core concepts / Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning.
Haynes, Teresa W., 1953- author.; Hedetniemi, S. T., author.; Henning, Michael A., author.
2023
QA166
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Title Domination in graphs : core concepts / Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning.
Author Haynes, Teresa W., 1953- author.
ISBN 9783031094965 (electronic bk.)
3031094964 (electronic bk.)
3031094956
9783031094958
DOI https://doi.org/10.1007/978-3-031-09496-5
Published Cham, Switzerland : Springer, 2023.
Language English
Description 1 online resource (1 volume) : illustrations (black and white, and color).
Item Number 10.1007/978-3-031-09496-5 doi
Call Number QA166
Dewey Decimal Classification 511/.5
Summary 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. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, theyve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, 2020 and Structures of Domination in Graphs, 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Hedetniemi, S. T., author.
Henning, Michael A., author.
Series Springer monographs in mathematics.
Available in Other Form DOMINATION IN GRAPHS.
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1. Introduction
2. Historic background
3. Domination Fundamentals
4. Bounds in terms of order and size, and probability
5. Bounds in terms of degree
6. Bounds with girth and diameter conditions
7. Bounds in terms of forbidden subgraphs
8. Domination in graph families : Trees
9. Domination in graph families: Claw-free graphs
10. Domination in regular graphs including Cubic graphs
11. Domination in graph families: Planar graph
12. Domination in graph families: Chordal, bipartite, interval, etc
13. Domination in grid graphs and graph products
14. Progress on Vizing's Conjecture
15. Sums and Products (Nordhaus-Gaddum)
16. Domination Games
17. Criticality
18. Complexity and Algorithms
19. The Upper Domination Number
20. Domatic Numbers (for lower and upper gamma) and other dominating partitions, including the newly introduced Upper Domatic Number
21. Concluding Remarks, Conjectures, and Open Problems.

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