Total Domination in Graphs

✍ Scribed by Michael A. Henning, Anders Yeo (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 184
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-8
Properties of Total Dominating Sets and General Bounds....Pages 9-17
Complexity and Algorithmic Results....Pages 19-29
Total Domination in Trees....Pages 31-38
Total Domination and Minimum Degree....Pages 39-54
Total Domination in Planar Graphs....Pages 55-58
Total Domination and Forbidden Cycles....Pages 59-64
Relating the Size and Total Domination Number....Pages 65-69
Total Domination in Claw-Free Graphs....Pages 71-75
Total Domination Number Versus Matching Number....Pages 77-81
Total Domination Critical Graphs....Pages 83-101
Total Domination and Graph Products....Pages 103-108
Graphs with Disjoint Total Dominating Sets....Pages 109-118
Total Domination in Graphs with Diameter Two....Pages 119-124
Nordhaus–Gaddum Bounds for Total Domination....Pages 125-129
Upper Total Domination....Pages 131-139
Variations of Total Domination....Pages 141-148
Conjectures and Open Problems....Pages 149-158
Back Matter....Pages 159-178

✦ Subjects

Graph Theory; Analysis; Number Theory