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© 2013

Total Domination in Graphs

Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Michael A. Henning, Anders Yeo
    Pages 1-8
  3. Michael A. Henning, Anders Yeo
    Pages 9-17
  4. Michael A. Henning, Anders Yeo
    Pages 19-29
  5. Michael A. Henning, Anders Yeo
    Pages 31-38
  6. Michael A. Henning, Anders Yeo
    Pages 39-54
  7. Michael A. Henning, Anders Yeo
    Pages 55-58
  8. Michael A. Henning, Anders Yeo
    Pages 59-64
  9. Michael A. Henning, Anders Yeo
    Pages 65-69
  10. Michael A. Henning, Anders Yeo
    Pages 71-75
  11. Michael A. Henning, Anders Yeo
    Pages 77-81
  12. Michael A. Henning, Anders Yeo
    Pages 83-101
  13. Michael A. Henning, Anders Yeo
    Pages 103-108
  14. Michael A. Henning, Anders Yeo
    Pages 109-118
  15. Michael A. Henning, Anders Yeo
    Pages 119-124
  16. Michael A. Henning, Anders Yeo
    Pages 125-129
  17. Michael A. Henning, Anders Yeo
    Pages 131-139
  18. Michael A. Henning, Anders Yeo
    Pages 141-148
  19. Michael A. Henning, Anders Yeo
    Pages 149-158
  20. Back Matter
    Pages 159-178

About this book

Introduction

Total Domination in Graphs gives a clear understanding  of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is  an excellent resource for students interested in beginning their research in this field.  Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems.

Keywords

Hypergraph Nordhaus-Gaddum Total Domination diameter-2-critical graphs

Authors and affiliations

  1. 1., Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa
  2. 2., Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa

About the authors

Michael Henning is a world-leader in domination theory in graphs. He has been a plenary and invited speaker at several international conferences and is a prolific researcher having published over 300 papers to date in international mathematics journals. Michael 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 Michael 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.


 

Anders Yeo is a world-leader in several areas within mathematics and computer science, including total domination in graphs and transversal in hypergraphs, digraphs, and in Fixed Parameter Tractability. He has been a plenary and invited speaker at several international conferences and is a prolific researcher having published over 130 papers to date in international mathematics journals. Anders was born in Australia and schooled in Denmark having obtained his PhD at Odense University in December 1997. Thereafter he pursued postdoctoral studies in the Department of Mathematics and Statistics at the University of Victoria in Canada for one year and postdoctoral studies in the Computer Science Department at the University of Aarhus in Denmark for a further two years. In September 2001 he began as a lecturer at Royal Holloway, University of London and was very rapidly promoted to Reader in March 2003 where he worked until January 2012. Anders is currently employed by the University of Johannesburg in a research capacity.

Bibliographic information

  • Book Title Total Domination in Graphs
  • Authors Michael A. Henning
    Anders Yeo
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI https://doi.org/10.1007/978-1-4614-6525-6
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-6524-9
  • Softcover ISBN 978-1-4899-9156-0
  • eBook ISBN 978-1-4614-6525-6
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XIV, 178
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Graph Theory
    Analysis
    Number Theory
  • Buy this book on publisher's site

Reviews

From the reviews:

“This book is a concise … lucid, and thorough survey on total domination. It is intended to bring graduate students and researchers up to date on results and techniques in the field … . It will be a valuable resource for those in the field or wishing to learn the field.” (William F. Klostermeyer, Mathematical Reviews, November, 2013)