Overview
- Surveys include known results with sample proof techniques for each parameter
- Generally focuses on primary dominating sets
- Provides a reference for established researchers and graduate students
Part of the book series: Developments in Mathematics (DEVM, volume 64)
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Table of contents (16 chapters)
Keywords
- Domination Chain
- Independent Domination
- Total Domination
- Paired Domination
- Connected Domination
- Restrained Domination
- Dominating Functions
- Roman Domination
- Rainbow Domination
- Alliances in Graphs
- Vizing's Conjecture for Domination Parameters
- Power Domination
- Broadcast Domination
- Distance Domination
- Multiple domination
- Irredundance in graphs
- Global Domination
- Secure Domination
- Strong and Weak Domination
- Exponential Domination
About this book
This volume comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The focus is on primary dominating sets such as paired domination, connected domination, restrained domination, dominating functions, Roman domination, and power domination. Additionally, surveys include known results with a sample of proof techniques for each parameter. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms; the second chapter provides an overview of models of domination from which the parameters are defined.
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 in the field and proof techniques used.
Editors and Affiliations
About the editors
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 Developments in Mathematics book Transversals in Linear Uniform Hypergraphs.
Bibliographic Information
Book Title: Topics in Domination in Graphs
Editors: Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-030-51117-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-51116-6Published: 09 November 2020
Softcover ISBN: 978-3-030-51119-7Published: 10 November 2021
eBook ISBN: 978-3-030-51117-3Published: 19 October 2020
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: VIII, 545
Number of Illustrations: 1 b/w illustrations, 49 illustrations in colour
Topics: Graph Theory