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.
General
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