Topics in Domination in Graphs

✍ Scribed by Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning

• Publisher: Springer International Publishing;Springer
• Year: 2020
• Tongue: English
• Leaves: 545
• Series: Developments in Mathematics 64
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-viii
Glossary of Common Terms (Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning)....Pages 1-12
Models of Domination in Graphs (Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning)....Pages 13-30
Paired Domination in Graphs (Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning)....Pages 31-77
Connected Domination (Mustapha Chellali, Odile Favaron)....Pages 79-127
Restrained and Total Restrained Domination in Graphs (Johannes H. Hattingh, Ernst J. Joubert)....Pages 129-150
Multiple Domination (Adriana Hansberg, Lutz Volkmann)....Pages 151-203
Distance Domination in Graphs (Michael A. Henning)....Pages 205-250
Locating-Domination and Identification (Antoine Lobstein, Olivier Hudry, Irène Charon)....Pages 251-299
Signed and Minus Dominating Functions in Graphs (Liying Kang, Erfang Shan)....Pages 301-348
Fractional Dominating Parameters (Wayne Goddard, Michael A. Henning)....Pages 349-363
Roman Domination in Graphs (Mustapha Chellali, Nader Jafari Rad, Seyed Mahmoud Sheikholeslami, Lutz Volkmann)....Pages 365-409
Rainbow Domination in Graphs (Boštjan Brešar)....Pages 411-443
Eternal and Secure Domination in Graphs (William F. Klostermeyer, C. M. Mynhardt)....Pages 445-478
Stratified Domination (Gary Chartrand, Ping Zhang)....Pages 479-496
Global Domination (Robert C. Brigham, Julie R. Carrington, Ronald D. Dutton)....Pages 497-519
Power Domination in Graphs (Paul Dorbec)....Pages 521-545

✦ Subjects

Mathematics; Graph Theory