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This book gives an overview of research on graphs associated with
commutative rings. The study of the connections between algebraic
structures and certain graphs, especially finite groups and their
Cayley graphs, is a classical subject which has attracted a lot of
interest. More recently, attention has focused on graphs
constructed from commutative rings, a field of study which has
generated an extensive amount of research over the last three
decades. The aim of this text is to consolidate this large body of
work into a single volume, with the intention of encouraging
interdisciplinary research between algebraists and graph theorists,
using the tools of one subject to solve the problems of the other.
The topics covered include the graphical and topological properties
of zero-divisor graphs, total graphs and their transformations, and
other graphs associated with rings. The book will be of interest to
researchers in commutative algebra and graph theory and anyone
interested in learning about the connections between these two
subjects.
This book gives an overview of research on graphs associated with
commutative rings. The study of the connections between algebraic
structures and certain graphs, especially finite groups and their
Cayley graphs, is a classical subject which has attracted a lot of
interest. More recently, attention has focused on graphs
constructed from commutative rings, a field of study which has
generated an extensive amount of research over the last three
decades. The aim of this text is to consolidate this large body of
work into a single volume, with the intention of encouraging
interdisciplinary research between algebraists and graph theorists,
using the tools of one subject to solve the problems of the other.
The topics covered include the graphical and topological properties
of zero-divisor graphs, total graphs and their transformations, and
other graphs associated with rings. The book will be of interest to
researchers in commutative algebra and graph theory and anyone
interested in learning about the connections between these two
subjects.
The concept of dominating sets introduced by Ore and Berge, is
currently receiving much attention in the literature of graph
theory. Several types of domination parameters have been studied by
imposing several conditions on dominating sets. Ore observed that
the complement of every minimal dominating set of a graph with
minimum degree at least one is also a dominating set. This implies
that every graph with minimum degree at least one has two disjoint
dominating sets. Recently several authors initiated the study of
the cardinalities of pairs of disjoint dominating sets in graphs.
The inverse domination number is the minimum cardinality of a
dominating set whose complement contains a minimum dominating set.
Motivated by the inverse domination number, there are studies which
deals about two disjoint domination number of a graph.
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