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Henning M.A., Yeo A. Total Domination in Graphs

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Henning M.A., Yeo A. Total Domination in Graphs
Springer Science+Business Media, New York, 2013. — 184 p. — (Springer Monographs in Mathematics) — ISBN: 1461465249

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.
Contents
Introduction
Properties of Total Dominating Sets and General Bounds
Complexity and Algorithmic Results
Total Domination in Trees
Total Domination and Minimum Degree
Total Domination in Planar Graphs
Total Domination and Forbidden Cycles
Relating the Size and Total Domination Number
Total Domination in Claw-Free Graphs
Total Domination Number Versus Matching Number
Total Domination Critical Graphs
Total Domination and Graph Products
Graphs with Disjoint Total Dominating Sets
1Total Domination in Graphs with Diameter Two
Nordhaus–Gaddum Bounds for Total Domination
Upper Total Domination
Variations of Total Domination
Conjectures and Open Problems
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