Groups as Graphs by Kandasamy & Smarandache

Book Contents :-
1. Introduction to Some Basic Concepts 1.1 Properties of Rooted Trees 1.2 Basic Concepts 2. Groups and Graphs 3. Identity Graphs of Some Algebraic Structures 3.1 Identity Graphs of Semigroups 3.2 Special Identity Graphs of Loops 3.3 The Identity Graph of a Finite Commutative Ring with Unit 4. Suggested Problems

About this book :-
"Groups as Graphs" by "W. B. V. Kandasamy" and "F. Smarandache" is a mathematical book that connects "group theory" with "graph theory". It explains how finite groups can be represented using graphs, making abstract algebra concepts easier to visualize and understand. The book introduces identity graphs and explores how group structures like subgroups and normal subgroups can be studied through graphical representations. This approach helps readers see relationships within algebraic systems in a more intuitive way. The book focuses on the idea that every finite group can be mapped to a graph where elements and connections reflect algebraic properties. By using "identity graphs" and other graph-based tools, the authors show how complex group properties become clearer. It also extends the discussion to semigroups and rings, demonstrating that graph representations can be useful beyond traditional group theory. Overall, "Groups as Graphs" is useful for students and researchers interested in the intersection of "mathematics" and "graph-based modeling". It provides a unique perspective on algebraic structures, helping readers analyze groups visually. The combination of group theory and graphs makes abstract ideas more accessible and opens new ways to study mathematical relationships. This book is valuable for anyone exploring modern approaches to algebra and discrete mathematics.

Book Detail :-
Title: Groups as Graphs by Kandasamy & Smarandache
Publisher: CuArt
Year: 2009
Pages: 170
Type: PDF
Language: English
ISBN-10 #: B08G8FQ4WG
ISBN-13 #: 978-9390367849
License: Arxiv License
Amazon: Amazon

About Author :-
The author Dr W.B. Vasantha Kandasamy is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai. In the past decade she has guided 11 Ph.D. scholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, four Ph.D. scholars are working under her guidance. Both authors have contributed significantly to modern mathematics. "W. B. V. Kandasamy" is known for research in algebra and fuzzy mathematics, while "Florentin Smarandache" has worked on neutrosophic logic and interdisciplinary mathematical models. Their collaboration in "algebra" and graph-based methods provides innovative perspectives on mathematical structures and applications.

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