Graphs from Rings
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Beschreibung
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.
This is the first monograph devoted to the construction of graphs from commutative rings Gives an overview of three decades of research in the subject Encourages interdisciplinary work between researchers in commutative algebra and discrete mathematics
Autor*in
David F. Anderson
Themen in »Graphs from Rings«
13-02,05-02, 05-12, 05C75, 05C10 Commutative Algebra Graph Theory Distance in graphs Structural characterization of family of graphs Planar graphs geometric and topological aspects of graph theory
Stimmen zu »Graphs from Rings«
“This book is really attractive, comprehensive, and full of valuable results for anyone working on the borderline between ring theory and graph theory.” (Mehrdad Nasernejad, Mathematical Reviews, April, 2023)
“This book is a very good survey of graphs defined on rings. The authors have collected results on almost all types of graphs related to rings. The book consists of ten chapters and an exhaustive bibliography of 443 items.” (S. K. Nimbhorkar, zbMATH 1486.13001, 2022)()