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Near Rings, Fuzzy Ideals, and Graph Theory

Author: Bhavanari Satyanarayana

Publisher: CRC Press

Published: 2013-05-21

Total Pages: 482

ISBN-13: 1439873100

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.

Near Rings, Fuzzy Ideals, and Graph Theory

Author: Bhavanari Satyanarayana

Publisher: CRC Press

Published: 2013-05-21

Total Pages: 480

ISBN-13: 1439873119

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Applied Linear Algebra, Probability and Statistics

Author: Ravindra B. Bapat

Publisher: Springer Nature

Published: 2023-07-31

Total Pages: 540

ISBN-13: 9819923107

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This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

Neutrosophic Fuzzy Ideals of Near-Rings

Author: A. Solairaju

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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In this paper, the notion of Neutrosophic fuzzy ideals of near-rings are introduced and discussed some algebraic properties like union ,intersection , homomorphic image and preimage of neutrosophic fuzzy ideals of near-rings. Further we discuss about the direct product of Neutrosophic fuzzy ideals of near-rings .

Near-rings: The Theory and its Applications

Author:

Publisher: Elsevier

Published: 2011-10-10

Total Pages: 469

ISBN-13: 9780080871349

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Near-rings: The Theory and its Applications

Nearrings, Nearfields And Related Topics

Author: Panackal Harikrishnan

Publisher: World Scientific

Published: 2016-11-28

Total Pages: 324

ISBN-13: 981320737X

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Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Smarandache Near-Rings

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

Published: 2002

Total Pages: 201

ISBN-13: 1931233667

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Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that's why we study them in this book. Thus, as a particular case: A Near-Ring is a non-empty set N together with two binary operations '+' and '.' such that (N, +) is a group (not necessarily abelian), (N, .) is a semigroup. For all a, b, c in N we have (a + b) . c = a . c + b . c. A Near-Field is a non-empty set P together with two binary operations '+' and '.' such that (P, +) is a group (not necessarily abelian), (P \ {0}, .) is a group. For all a, b, c I P we have (a + b) . c = a . c + b . c. A Smarandache Near-ring is a near-ring N which has a proper subset P in N, where P is a near-field (with respect to the same binary operations on N).

Graph Theory and Its Applications

Author: G. Sethuraman

Publisher: Alpha Science Int'l Ltd.

Published: 2004

Total Pages: 208

ISBN-13: 9788173195693

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Contributed papers presented at the Conference on Graph Theory and its Applications, held on March 14-16, 2001, at Anna University, Chennai.

Graph Theory and Its Applications

Author: Jonathan L. Gross

Publisher: CRC Press

Published: 2018-11-05

Total Pages: 577

ISBN-13: 0429757093

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Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

Graphs from Rings

Author: David F. Anderson

Publisher: Springer

Published: 2022-11-02

Total Pages: 0

ISBN-13: 9783030884123

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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.