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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.
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.
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, (c) 2020 and Structures of
Domination in Graphs, (c) 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.
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.
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.
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