Total Domination in Graphs [electronic resource] / by Michael A. Henning, Anders Yeo.
Contributor(s): Yeo, Anders [author.] | SpringerLink (Online service)Material type: TextSeries: Springer Monographs in Mathematics: Publisher: New York, NY : Springer New York : Imprint: Springer, 2013Description: XIV, 178 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461465256Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Number theory | Graph theory | Mathematics | Graph Theory | Analysis | Number TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 511.5 LOC classification: QA166-166.247Online resources: Click here to access online
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1. Introduction -- 2. Properties of Total Dominating Sets and General Bounds -- 3. Complexity and Algorithmic Results -- 4.Total Domination in Trees -- 5.Total Domination and Minimum Degree -- 6. Total Domination in Planar Graphs -- 7. Total Domination and Forbidden Cycles -- 8. Relating the Size and Total Domination Number -- 9. Total Domination in Claw-Free Graphs -- 10. Total Domination Number versus Matching Number -- 11. Total Domination Critical Graphs -- 12. Total Domination and Graph Products -- 13. Graphs with Disjoint Total Dominating Sets -- 14. Total Domination in Graphs with Diameter Two -- 15. Nordhaus-Gaddum Bounds for Total Domination -- 16. Upper Total Domination -- 17.Variations of Total Domination -- 18. Conjectures and Open Problems -- Index.
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.