This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms.

The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.

Autorentext
Teresa W. Haynes has focused her research on domination in graphs for over 30 years and is perhaps best known for coauthoring the 1998 book Fundamentals of Domination in Graphs and the companion volume Domination in Graphs: Advanced Topics. She has also co-edited 2 volumes in Springer's Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Haynes is also a co-author of the Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi. Upon receiving her PhD from the University of Central Florida in 1988, she joined East Tennessee State University, where she is currently professor in the Department of Mathematics and Statistics. Haynes has coauthored more than 200 papers on domination and domination-related concepts, which introduced some of the most studied concepts in domination, such as power domination, paired domination, double domination, alliances and broadcasts in graphs, and stratified domination.

**Stephen T. Hedetniemi is one of the earliest pioneers of domination in graphs along with E. J. Cockayne, who together proposed the theory of domination in graphs, in one of the most cited papers in the field in 1977. He received his PhD from the University of Michigan in 1966, with two world-class advisors, graph theorist Frank Harary, and the pioneer of genetic algorithms and MacArthur Fellowship winner, John Holland. He coauthored, the first book on domination in 1988 Fundamentals of Domination in Graphs, and co-edited a second book, Domination in Graphs: Advanced Topics. He also co-edited 2 volumes in Springer's Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Since 1974 he has coauthored more than 300 papers, 180 of which are on domination and domination-related concepts. Hedetniemi has introduced some of the most-studied concepts in domination theory, including total domination, independent domination, irredundance, Roman domination, power domination, alliances in graphs, signed and minus domination, fractional domination, domatic numbers, domination in grid graphs and chessboards, the first domination algorithms, the first domination NP-completeness results, and the first self-stabilizing domination algorithms. After leaving the University of Michigan, he taught computer science at the University of Iowa, and the University of Virginia, spent a visiting year at the University of Victoria with E. J. Cockayne, and then became department head of Computer and information Science at the University of Oregon. Since 1982 has been at Clemson University, where he served a five-year term as department head, and served on the Executive Committee of the Computing Accreditation Commission of ABET, Inc. He is currently Emeritus Professor of Computer Science in the School of Computing at Clemson University.

**Michael A. Henning has devoted much of his research interests to the field of domination theory in graphs. He has been both plenary and invited speakers at several international conferences and is a prolific researcher having published over 460 papers to date in international mathematics journals. Henning was born and schooled in South Africa having obtained his PhD at the University of Natal in April 1989. In January 1989, he started his academic career as a lecturer at the University of Zululand, before accepting a lectureship in mathematics at the former University of Natal in January 1991. In January 2000, he was appointed a full professor at the University of Natal, which later merged with the University of Durban-Westville to form the University of KwaZulu-Natal in January 2004. After spending almost 20 years at the University of KwaZulu-Natal and one of its predecessors, the University of Natal, Michael moved to the University of Johannesburg in May 2010 as a research professor. He co-authored a Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi and co-authored the Springer Monographs in Mathematics book Total Domination in Graphs and in 2020, he co-authored Springer's **...

Inhalt

1. Glossary of Common Terms (Haynes).- Part 1. Related Parameters: 2. Broadcast Domination in Graphs (MacGillivray).- 3. Alliances and Related Domination Parameters (Haynes).- 4. Fractional Domatic, Idomatic and Total Domatic Numbers of a Graph (Goddard).- 5. Dominator and Total Dominator Colorings in Graphs (Henning).- 6. Irredundance (Mynhardt).- 7. The Private Neighbor Concept (McRae).- 8. An Introduction to Game Domination in Graphs (Henning).- 9. Domination and Spectral Graph Theory (Hoppen).- 10. Varieties of Roman Domination (Chellali).- Part 2. Domination in Selected Graph Families: 11. Domination and Total Domination in Hypergraphs (Yeo).- 12. Domination in Chessboards (Hedetniemi).- 13. Domination in Digraphs (Haynes).- Part 3. Algorithms and Complexity: 14. Algorithms and Complexity of Signed, Minus and Majority Domination (McRae).- 15. Algorithms and Complexity of Power Domination in Graphs (Mohan).- 16. Self-Stabilizing Domination Algorithms (Hedetniemi).- 17. Algorithms and Complexity of Alliances in Graphs (Hedetniemi)