Domination In Graphs Core Concepts

Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
Publisher : Springer
Page : 0 pages
File Size : 48,5 Mb
Release : 2023-04-30
Category : Mathematics
ISBN : 3031094956

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Domination in Graphs: Core Concepts by Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning Pdf

This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they’ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.

Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
Publisher : Springer Nature
Page : 655 pages
File Size : 49,9 Mb
Release : 2023-04-29
Category : Mathematics
ISBN : 9783031094965

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Domination in Graphs: Core Concepts by Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning Pdf

This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they’ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.

Author : Teresa W. Haynes,Stephen Hedetniemi,Peter Slater
Publisher : CRC Press
Page : 465 pages
File Size : 41,5 Mb
Release : 2013-12-16
Category : Mathematics
ISBN : 9781482246582

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Fundamentals of Domination in Graphs by Teresa W. Haynes,Stephen Hedetniemi,Peter Slater Pdf

"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 : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
Publisher : Springer Nature
Page : 536 pages
File Size : 40,9 Mb
Release : 2021-05-04
Category : Mathematics
ISBN : 9783030588922

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Structures of Domination in Graphs by Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning Pdf

This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms. 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 and proof techniques used in the field.

Author : Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning
Publisher : Springer Nature
Page : 545 pages
File Size : 45,7 Mb
Release : 2020-10-19
Category : Mathematics
ISBN : 9783030511173

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Topics in Domination in Graphs by Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Henning Pdf

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 : TeresaW. Haynes
Publisher : Routledge
Page : 507 pages
File Size : 54,7 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351454636

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Domination in Graphs by TeresaW. Haynes Pdf

""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 : C. Y. Ponnappan
Publisher : Archers & Elevators Publishing House
Page : 128 pages
File Size : 47,9 Mb
Release : 2024-07-03
Category : Antiques & Collectibles
ISBN : 9788194706519

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Studies in Graph Theory: Support Domination in Graphs and Related Concepts by C. Y. Ponnappan Pdf

Author : Michael A. Henning,Anders Yeo
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 49,8 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781461465256

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Total Domination in Graphs by Michael A. Henning,Anders Yeo Pdf

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 : Boštjan Brešar,Michael A. Henning,Sandi Klavžar,Douglas F. Rall
Publisher : Springer Nature
Page : 131 pages
File Size : 54,7 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783030690878

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Domination Games Played on Graphs by Boštjan Brešar,Michael A. Henning,Sandi Klavžar,Douglas F. Rall Pdf

This concise monograph present the complete history of the domination game and its variants up to the most recent developments and will stimulate research on closely related topics, establishing a key reference for future developments. The crux of the discussion surrounds new methods and ideas that were developed within the theory, led by the imagination strategy, the Continuation Principle, and the discharging method of Bujtás, to prove results about domination game invariants. A toolbox of proof techniques is provided for the reader to obtain results on the domination game and its variants. Powerful proof methods such as the imagination strategy are presented. The Continuation Principle is developed, which provides a much-used monotonicity property of the game domination number. In addition, the reader is exposed to the discharging method of Bujtás. The power of this method was shown by improving the known upper bound, in terms of a graph's order, on the (ordinary) domination number of graphs with minimum degree between 5 and 50. The book is intended primarily for students in graph theory as well as established graph theorists and it can be enjoyed by anyone with a modicum of mathematical maturity. The authors include exact results for several families of graphs, present what is known about the domination game played on subgraphs and trees, and provide the reader with the computational complexity aspects of domination games. Versions of the games which involve only the “slow” player yield the Grundy domination numbers, which connect the topic of the book with some concepts from linear algebra such as zero-forcing sets and minimum rank. More than a dozen other related games on graphs and hypergraphs are presented in the book. In all these games there are problems waiting to be solved, so the area is rich for further research. The domination game belongs to the growing family of competitive optimization graph games. The game is played by two competitors who take turns adding a vertex to a set of chosen vertices. They collaboratively produce a special structure in the underlying host graph, namely a dominating set. The two players have complementary goals: one seeks to minimize the size of the chosen set while the other player tries to make it as large as possible. The game is not one that is either won or lost. Instead, if both players employ an optimal strategy that is consistent with their goals, the cardinality of the chosen set is a graphical invariant, called the game domination number of the graph. To demonstrate that this is indeed a graphical invariant, the game tree of a domination game played on a graph is presented for the first time in the literature.

Author : J. Michael Ryan
Publisher : John Wiley & Sons
Page : 450 pages
File Size : 50,5 Mb
Release : 2018-09-07
Category : Social Science
ISBN : 9781119168638

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Core Concepts in Sociology by J. Michael Ryan Pdf

An essential guide to the basic concepts that comprise the study of sociology with contributions from an international range of leading experts Core Concepts in Sociology is a comprehensive guide to the essential concepts relevant to the current study of the discipline and wider social science. The contributing authors cover a wide range of concepts that remain at the heart of sociology including those from its academic founding and others much more recent in their development. The text contains contributions from an international panel of leading figures in the field, utilizing their expertise on core concepts and presenting an accessible introduction for students. Drawing on the widest range of ideas, research, current literature and expert assessment, Core Concepts in Sociology contains over 90 concepts that represent the discipline. Coverage includes concepts ranging from aging to capitalism, democracy to economic sociology, epistemology to everyday life, media to risk, stigma and much more. This vital resource: Sets out the concepts that underpin the study of sociology and wider social science Contains contributions from an international panel of leading figures in the field Includes a comprehensive review of the basic concepts that comprise the foundation and essential development of the discipline Designed as a concise and accessible resource Written for students, researchers and wider professionals with an interest in the field of sociology, Core Concepts in Sociology offers a concise, affordable and accessible resource for studying the underpinnings of sociology and social science.

Author : S.T. Hedetniemi,R.C. Laskar
Publisher : Elsevier
Page : 277 pages
File Size : 50,5 Mb
Release : 1991-02-01
Category : Mathematics
ISBN : 008086788X

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Topics on Domination by S.T. Hedetniemi,R.C. Laskar Pdf

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 : B.Basavanagoud,Sujata Timmanaikar
Publisher : Infinite Study
Page : 10 pages
File Size : 41,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 8210379456XXX

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Accurate Independent Domination in Graphs by B.Basavanagoud,Sujata Timmanaikar Pdf

In this paper, we initiate a study of this new parameter and obtain some results concerning this parameter.

Author : Ismael González Yero
Publisher : MDPI
Page : 146 pages
File Size : 52,7 Mb
Release : 2020-11-18
Category : Mathematics
ISBN : 9783039435159

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Distances and Domination in Graphs by Ismael González Yero Pdf

This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present.

Author : Manju Raju
Publisher : Independent Author
Page : 0 pages
File Size : 41,6 Mb
Release : 2023-02-03
Category : Electronic
ISBN : 1805249975

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Domination in Graphs Theory and Applications by Manju Raju Pdf

In this chapter we collect some basic definitions and the-orems on graphs and hypergraphs which are needed for the subse-quent chapters. For graph theoretic terminology we refer to Chartrand and Lesniak [8] and for hypergraphs, we basically use the terminology of Berge [4, 5]. In Section 1.2 we give a brief outline of the basic definitions in graph theory and present the concept of minimal and maximal P-sets, where Pis a graph theoretic property concerning subsets of the vertex set V. In Section 1.3 we give a brief outline of the basic definitions in hypergraph theory, and in section 1.4 we present the fundamentals of domination in graphs and list some of the theo-rems that we use in subsequent chapters. In Section 1.5 we deal with algorithmic aspects, complexity results and NP-completeness. In Section 1.6 we present an overview of the organization of the remaining chapters of the book.

Author : Robert Meersman,Tharam Dillon,Pilar Herrero,Akhil Kumar,Manfred Reichert,Li Qing,Beng Chin Ooi,Ernesto Damiani,Douglas C. Schmidt,Jules White,Manfred Hauswirth,Pascal Hitzler,Mukesh K. Mohania
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 41,7 Mb
Release : 2011-11-09
Category : Computers
ISBN : 9783642251054

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On the Move to Meaningful Internet Systems: OTM 2011 by Robert Meersman,Tharam Dillon,Pilar Herrero,Akhil Kumar,Manfred Reichert,Li Qing,Beng Chin Ooi,Ernesto Damiani,Douglas C. Schmidt,Jules White,Manfred Hauswirth,Pascal Hitzler,Mukesh K. Mohania Pdf

The two-volume set LNCS 7044 and 7045 constitutes the refereed proceedings of three confederated international conferences: Cooperative Information Systems (CoopIS 2011), Distributed Objects and Applications - Secure Virtual Infrastructures (DOA-SVI 2011), and Ontologies, DataBases and Applications of SEmantics (ODBASE 2011) held as part of OTM 2011 in October 2011 in Hersonissos on the island of Crete, Greece. The 55 revised full papers presented were carefully reviewed and selected from a total of 141 submissions. The 28 papers included in the second volume constitute the proceedings of DOA-SVI 2011 with 15 full papers organized in topical sections on performance measurement and optimization, instrumentation, monitoring, and provisioning, quality of service, security and privacy, and models and methods, and ODBASE 2011 with 9 full papers organized in topical sections on acquisition of semantic information, use of semantic information, and reuse of semantic information and 4 short papers.