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Graphs from rings

Anderson, David F.

Graphs from rings

Record Type:	Electronic resources : Monograph/item
Title/Author:	Graphs from ringsby David F. Anderson ... [et al.].
other author:	Anderson, David F.
Published:	Cham :Springer International Publishing :2021.
Description:	xvi, 538 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Commutative rings.
Online resource:	https://doi.org/10.1007/978-3-030-88410-9
ISBN:	9783030884109$q(electronic bk.)

Graphs from rings
Graphs from rings[electronic resource] /by David F. Anderson ... [et al.]. - Cham :Springer International Publishing :2021. - xvi, 538 p. :ill., digital ;24 cm.

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$q(electronic bk.)

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

237116
Commutative rings.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Graphs from rings
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260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xvi, 538 p. : $b ill., digital ; $c 24 cm.
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.
650 0 $a Commutative rings. $3 237116
650 0 $a Graph theory. $3 181880
650 1 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Graph Theory. $3 522732
700 1 $a Anderson, David F. $3 237563
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773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-88410-9
950 $a Mathematics and Statistics (SpringerNature-11649)