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Graphs from Rings

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Graphs from Rings/ by David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam.
Author:	Anderson, David F.
other author:	Asir, T.
Description:	XVI, 538 p. 87 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Commutative algebra. -
Online resource:	https://doi.org/10.1007/978-3-030-88410-9
ISBN:	9783030884109

Graphs from Rings
Anderson, David F.

Graphs from Rings[electronic resource] /by David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam. - 1st ed. 2021. - XVI, 538 p. 87 illus.online resource.

Introduction -- Distances in zero-divisor graphs -- Properties of zero-divisor graphs -- Genus of zero-divisor graphs -- Zero-divisor graph generalizations -- Total graphs of commutative rings -- Graphs from total graphs -- Generalized total graphs -- Other graphs associated with rings -- Bibliography -- Index.

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.

ISBN: 9783030884109

Standard No.: 10.1007/978-3-030-88410-9doiSubjects--Topical Terms:

672047
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Graphs from Rings
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505 0 $a Introduction -- Distances in zero-divisor graphs -- Properties of zero-divisor graphs -- Genus of zero-divisor graphs -- Zero-divisor graph generalizations -- Total graphs of commutative rings -- Graphs from total graphs -- Generalized total graphs -- Other graphs associated with rings -- Bibliography -- Index.
520 $a 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.
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