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Author: Dr. D. D. Pandya Publisher: OrangeBooks Publication ISBN: Category : Young Adult Nonfiction Languages : en Pages : 88
Book Description
In this thesis we have discussed variants of domination like vertex covering, Independent domination, K domination, K dependent set , K-dependent K domination, Total domination, Extended total domination, K-tuple domination, Total K domination, Restrained domination and Total restrained domination. We have characterized edges whose removal affects or does not affect these variants. We have also discussed changing and unchanging of these variants in terms of edge addition between two non – adjacent vertices. From history we can see that much work has been done for critical graphs but existing work is related to all edges of graph. But for application point of view sometimes we require to delete or add any particular edge. So our work is related to any particular edge but it is applicable for all graphs. When existing work for critical graphs is applicable for any edge but in some particular graph. In this way our results carry more important when any particular edge is to be focused. We have also discussed bondage number for some variants. Our results are related to relation between vertices and edges whose removal affects all these variants. Many research papers have been published for criticalness of graph with respect to vertex removal. So our results may be link between vertices and edge removal. It will insist many research scholars to do work in this direction. We believe our study will become instrumental in making the relation between edge removal and vertex removal more transparent and effectively. We hope our thesis provide row material for other research scholars of engineering field also.
Author: Dr. D. D. Pandya Publisher: OrangeBooks Publication ISBN: Category : Young Adult Nonfiction Languages : en Pages : 88
Book Description
In this thesis we have discussed variants of domination like vertex covering, Independent domination, K domination, K dependent set , K-dependent K domination, Total domination, Extended total domination, K-tuple domination, Total K domination, Restrained domination and Total restrained domination. We have characterized edges whose removal affects or does not affect these variants. We have also discussed changing and unchanging of these variants in terms of edge addition between two non – adjacent vertices. From history we can see that much work has been done for critical graphs but existing work is related to all edges of graph. But for application point of view sometimes we require to delete or add any particular edge. So our work is related to any particular edge but it is applicable for all graphs. When existing work for critical graphs is applicable for any edge but in some particular graph. In this way our results carry more important when any particular edge is to be focused. We have also discussed bondage number for some variants. Our results are related to relation between vertices and edges whose removal affects all these variants. Many research papers have been published for criticalness of graph with respect to vertex removal. So our results may be link between vertices and edge removal. It will insist many research scholars to do work in this direction. We believe our study will become instrumental in making the relation between edge removal and vertex removal more transparent and effectively. We hope our thesis provide row material for other research scholars of engineering field also.
Author: S.T. Hedetniemi Publisher: Elsevier ISBN: 008086788X Category : Mathematics Languages : en Pages : 287
Book Description
The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other domination-related parameters) can be computed in polynomial time.
Author: TeresaW. Haynes Publisher: Routledge ISBN: 1351454641 Category : Mathematics Languages : en Pages : 519
Book Description
""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.
Author: Teresa W. Haynes Publisher: Springer Nature ISBN: 3030511170 Category : Mathematics Languages : en Pages : 545
Book Description
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.
Author: Michael A. Henning Publisher: Springer Science & Business Media ISBN: 1461465257 Category : Mathematics Languages : en Pages : 184
Book Description
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.
Author: M. H. Akhbari Publisher: Infinite Study ISBN: Category : Languages : en Pages : 13
Book Description
In this paper, we obtain the domination number, the total domination number and the independent domination number in the neighborhood graph. We also investigate these parameters of domination on the join and the corona of two neighborhood graphs.
Author: T Tamizh Chelvam Publisher: LAP Lambert Academic Publishing ISBN: 9783844315813 Category : Languages : en Pages : 172
Book Description
For the last thirty years, due to the involvement in areas such as computer science, electrical and computer engineering and operations research, graph theory has grown exponentially. Study of domination is one of the important sub-areas of graph theory and seen enormous growth due to its varied applications. The study on domination not only restricted to domination parameters, but also relates to the other parameters like independence number, covering number and others. This book deals with certain new domination parameters and their properties with other existing parameters of graphs.
Author: Gary Chartrand Publisher: Springer Nature ISBN: 3030311104 Category : Mathematics Languages : en Pages : 94
Book Description
This book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning cycles and circuits, and distance that grew out of research topics investigated by Stephen Hedetniemi. The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas. The most important features deal with material, results, and problems that researchers may not be aware of but may find of interest. Each chapter contains results, methods and information that will give readers the necessary background to investigate each topic in more detail.
Author: Teresa W. Haynes Publisher: CRC Press ISBN: 1482246589 Category : Mathematics Languages : en Pages : 465
Book Description
"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."
Author: Dr. D. D. Pandya
Author: Dr. D. D. Pandya
Author: S.T. Hedetniemi
Author: TeresaW. Haynes
Author: Teresa W. Haynes
Author: Michael A. Henning
Author: M. H. Akhbari
Author: T Tamizh Chelvam
Author: Mark Schurch
Author: Gary Chartrand
Author: Teresa W. Haynes