Groups as Graphs by Kandasamy & Smarandache
Groups as Graphs - Table of Contents
PART I: GRAPH CONCEPTS & GROUPS
- 1. Introduction to Some Basic Concepts
- 1.1 Properties of Rooted Trees
- 1.2 Basic Concepts in Graph Theory
- 2. Groups and Graphs Representations
PART II: IDENTITY GRAPHS & PROBLEMS
- 3. Identity Graphs of Some Algebraic Structures
- 3.1 Identity Graphs of Semigroups
- 3.2 Special Identity Graphs of Loops
- 3.3 Identity Graph of Finite Commutative Rings
- 4. Suggested Problems and Exercises
What You Will Learn in Groups as Graphs
Groups as Graphs by W. B. Vasantha Kandasamy and Florentin Smarandache is an innovative, project-driven mathematical monograph that introduces visual and graph-theoretic representations for fundamental algebraic systems. This comprehensive volume guides readers through rooted tree properties, Cayley group graphs, identity graphs of semigroups, special loop graphs, and commutative ring identity structures with exceptional visual clarity and logical rigor.
Designed for graduate students, graph theorists, abstract algebraists, and computer science researchers, this foundational text reformulates abstract algebraic identities into clear graph-theoretic topologies. The authors provide step-by-step constructions for visualizing group elements, identity relations, and algebraic operations using graph vertices and directed edges. Whether you are studying algebraic graph invariants, non-associative loops, or network topologies, this book offers an indispensable roadmap.
Recognized globally for its open-access pedagogical approach to visual abstract algebra, it remains one of the best visual group theory books for self-study. By bridging discrete graph representations with modern abstract algebra, it serves as an essential tool for mastering algebraic group graphs with confidence.
Book Details & Specifications
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 the Author: Dr W. B. Vasantha Kandasamy
The author Dr W. B. Vasantha Kandasamy
is a prominent Indian mathematician and former professor at the Indian Institute of Technology (IIT) Madras, internationally recognized for her extensive research in abstract algebra, neutrosophic logic, fuzzy algebraic structures, and algebraic coding theory. She has authored over 100 research monographs and hundreds of research papers spanning pure mathematics and applied computer science.
Co-authored alongside Florentin Smarandache, Professor Emeritus of Mathematics at the University of New Mexico, Groups as Graphs reflects their long-standing research collaboration in pioneering open-access mathematical monographs. Their focus on visual representation, concrete structural examples, and accessible graph definitions makes this text a classic reference for visual group theory that continues to inspire research mathematicians and self-directed learners worldwide.
Read or Downloadable Groups as Graphs
Group Theory