Graphs From Rings

Author : David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam
Publisher : Springer Nature
Page : 548 pages
File Size : 46,5 Mb
Release : 2021-10-31
Category : Mathematics
ISBN : 9783030884109

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Graphs from Rings by David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam Pdf

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.

Author : David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 2021
Category : Electronic
ISBN : 3030884112

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Graphs from Rings by David F. Anderson,T. Asir,Ayman Badawi,T. Tamizh Chelvam Pdf

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.

Author : Bhavanari Satyanarayana,Kuncham Syam Prasad
Publisher : CRC Press
Page : 482 pages
File Size : 51,7 Mb
Release : 2013-05-21
Category : Computers
ISBN : 9781439873106

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Near Rings, Fuzzy Ideals, and Graph Theory by Bhavanari Satyanarayana,Kuncham Syam Prasad Pdf

Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations. After introducing all of the necessary fundamentals of algebraic systems, the book presents the essentials of near rings theory, relevant examples, notations, and simple theorems. It then describes the prime ideal concept in near rings, takes a rigorous approach to the dimension theory of N-groups, gives some detailed proofs of matrix near rings, and discusses the gamma near ring, which is a generalization of both gamma rings and near rings. The authors also provide an introduction to fuzzy algebraic systems, particularly the fuzzy ideals of near rings and gamma near rings. The final chapter explains important concepts in graph theory, including directed hypercubes, dimension, prime graphs, and graphs with respect to ideals in near rings. Near ring theory has many applications in areas as diverse as digital computing, sequential mechanics, automata theory, graph theory, and combinatorics. Suitable for researchers and graduate students, this book provides readers with an understanding of near ring theory and its connection to fuzzy ideals and graph theory.

Author : Sumi T,Anto A M
Publisher : Eliva Press
Page : 0 pages
File Size : 48,8 Mb
Release : 2023-06-08
Category : Electronic
ISBN : 9994988557

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The Graphs Associated with Rings by Sumi T,Anto A M Pdf

A ring is an abstract structure with a commutative addition, and a multiplication which may or may not be commutative. This distinction yields two quite different theories: the theory of respectively commutative or non-commutative rings. These notes are mainly concerned about commutative rings. Non-commutative rings have been an object of systematic study only quite recently, during the 20th century. Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points does not matter. Each object in a graph is called a node. The subject of graph theory had its beginnings in recreational math problems (see number game), but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science. The study of algebraic structures using the properties of graphs becomes an exciting research topic in the past twenty years, leading to many fascinating results and questions. There are many papers on assigning a graph to a group or a ring. Also, investigation of algebraic properties of groups or rings using the associated graph becomes an exciting topic. In 1999, the zero-divisor graph of a commutative ring Γ(R) was defined by David F. Anderson and Paul S. Livingston as the undirected graph with vertex set Z(R)∗, in which there is an arc from x to y if and only if xy = 0. Through this book, we illustrate some results about the Graphs associated with Rings.

Author : Ayman Badawi,Jim Coykendall
Publisher : Springer Nature
Page : 317 pages
File Size : 41,7 Mb
Release : 2022-03-11
Category : Mathematics
ISBN : 9789811684227

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Rings, Monoids and Module Theory by Ayman Badawi,Jim Coykendall Pdf

This book contains select papers on rings, monoids and module theory which are presented at the 3rd International Conference on Mathematics and Statistics (AUS-ICMS 2020) held at the American University of Sharjah, United Arab Emirates, from 6–9 February 2020. This conference was held in honour of the work of the distinguished algebraist Daniel D. Anderson. Many participants and colleagues from around the world felt it appropriate to acknowledge his broad and sweeping contributions to research in algebra by writing an edited volume in his honor. The topics covered are, inevitably, a cross-section of the vast expansion of modern algebra. The book is divided into two sections—surveys and recent research developments—with each section hopefully offering symbiotic utility to the reader. The book contains a balanced mix of survey papers, which will enable expert and non-expert alike to get a good overview of developments across a range of areas of algebra. The book is expected to be of interest to both beginning graduate students and experienced researchers.

Author : Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 50,9 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9781441969903

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Commutative Algebra by Marco Fontana,Salah-Eddine Kabbaj,Bruce Olberding,Irena Swanson Pdf

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

Author : P. Balasubramaniam,Kuru Ratnavelu,Grienggrai Rajchakit,G. Nagamani
Publisher : Springer Nature
Page : 349 pages
File Size : 47,7 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9789811660184

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Mathematical Modelling and Computational Intelligence Techniques by P. Balasubramaniam,Kuru Ratnavelu,Grienggrai Rajchakit,G. Nagamani Pdf

This book collects papers presented at the International Conference on Mathematical Modelling and Computational Intelligence Techniques (ICMMCIT) 2021, held at the Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, India, from 10–12 February 2021. Significant contributions from renowned researchers from fields of applied analysis, mathematical modelling and computing techniques have been received for this conference. Chapters emphasize on the research of computational nature focusing on new algorithms, their analysis and numerical results, as well as applications in physical, biological, social, and behavioural sciences. The accepted papers are organized in topical sections as mathematical modelling, image processing, control theory, graphs and networks, and inventory control.

Author : N. P. Shrimali,Nita H. Shah
Publisher : CRC Press
Page : 411 pages
File Size : 54,7 Mb
Release : 2020-11-09
Category : Computers
ISBN : 9781000210187

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Recent Advancements in Graph Theory by N. P. Shrimali,Nita H. Shah Pdf

Graph Theory is a branch of discrete mathematics. It has many applications to many different areas of Science and Engineering. This book provides the most up-to-date research findings and applications in Graph Theory. This book focuses on the latest research in Graph Theory. It provides recent findings that are occurring in the field, offers insights on an international and transnational levels, identifies the gaps in the results, and includes forthcoming international studies and research, along with its applications in Networking, Computer Science, Chemistry, and Biological Sciences, etc. The book is written with researchers and post graduate students in mind.

Author : D Bonchev
Publisher : CRC Press
Page : 310 pages
File Size : 50,9 Mb
Release : 1991-01-01
Category : Science
ISBN : 0856264547

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Chemical Graph Theory by D Bonchev Pdf

Initiates an ongoing series intended to consider a wide range of topics related to the mathematics of chemistry. Presents the fundamentals of graph theory and specific chemical applications of its. The topics include historical background, basic ideas and mathematical formalism, graph theory's influence in the rationalization of chemical nomenclature, graph-theoretical polynomials, and the interplay with molecular orbital theory in terms of graph spectral theory and topological resonance. Suitable for advanced undergraduates, graduates, and professionals. Acidic paper. Book club price, $52. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Derek Allan Holton,Charles H. C. Little
Publisher : Unknown
Page : 7 pages
File Size : 46,9 Mb
Release : 1980
Category : Graph theory
ISBN : 0868393061

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Regular Odd Rings and Non-planar Graphs by Derek Allan Holton,Charles H. C. Little Pdf

Author : Charles H. C. Little,Derek Allan Holton
Publisher : Unknown
Page : 12 pages
File Size : 48,6 Mb
Release : 1980
Category : Rings (Algebra)
ISBN : 0868393703

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Rings of Cutsets in Graphs by Charles H. C. Little,Derek Allan Holton Pdf

Author : ELHAM MEHDI-NEZHAD,AMIR M. RAHIMI
Publisher : Infinite Study
Page : 12 pages
File Size : 53,5 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 8210379456XXX

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THE SMARANDACHE VERTICES OF THE COMAXIMAL GRAPH OF A COMMUTATIVE RING by ELHAM MEHDI-NEZHAD,AMIR M. RAHIMI Pdf

The main object of this paper is to study the S-vertices of CG(R) and CG2(R) \ J(R) (or CGJ (R) for short), where CG2(R) is the subgraph of CG(R) which consists of nonunit elements of R and J(R) is the Jacobson radical of R. There is also a discussion on a relationship between the diameter and S-vertices of CGJ (R).

Author : Ayman Badawi
Publisher : Nova Publishers
Page : 220 pages
File Size : 49,6 Mb
Release : 2006
Category : Mathematics
ISBN : 1600210651

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Focus on Commutative Rings Research by Ayman Badawi Pdf

Focus on Commutative Rings Research

Author : Peter Widmayer,Gabriele Neyer,Stephan Eidenbenz
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 51,5 Mb
Release : 1999-10-27
Category : Computers
ISBN : 9783540667315

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Graph-Theoretic Concepts in Computer Science by Peter Widmayer,Gabriele Neyer,Stephan Eidenbenz Pdf

This book constitutes the refereed proceedings of the 25th International Workshop on Graph-Theorie Concepts in Computer Science WG'99, held at the Centre Stefano Frascini on Monte Verita, Ascona, Switzerland in June 1999. The 33 revised full papers presented together with four invited contributions were carefully reviewed and selected from 64 papers submitted. The papers provide a wealth of new results for various graph classes, graph computations, graph algorithms and graph-theoretical applications in a variety of fields.

Author : Brewer
Publisher : CRC Press
Page : 118 pages
File Size : 45,9 Mb
Release : 1981-04-01
Category : Mathematics
ISBN : 082476952X

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Power Series over Commutative Rings by Brewer Pdf