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A BRIEF COURSE ON GRAPH THEORY

Dr. B.C. Chakraborty & Dr. S. Chakraborty

First Published: 2022

ISBN: 978-93-94107-07-6

Pages: 336

**CONTENTS**

- Graphs and Digraphs

- Walk, Path, Cycle, Isomorphism, Matrix representation

- Connected Graphs and Connectivity

- Bipartite graphs and Matching

- Eulerian and Hamiltonian Graphs

- Shortest Path Problems, Travelling Salesman’s Problem, Chinese Postman Problem

- Tree

- Binary Tree, Tree traversal, and Binary Search Tree

- Planar Graphs

- Graph Colouring

- Answers

- Bibliography

- Index

**ABOUT THE BOOK**:

This book is written as a textbook for undergraduate and postgraduate students of one or two-semester preliminary courses in Graph Theory. This book may also be useful to students of Computer Science, Information Technology, and Engineering. The book covers most of the introductory and essential topics in Graph Theory which are followed by most Indian universities.

The book does not require any special background in Mathematics except some elementary concepts from Set theory, Matrix algebra, Method of Induction, and a certain amount of ‘mathematical maturity’ of Higher Secondary level.

The book contains ten chapters. The first chapter deals with Graphs and Digraphs. The subsequent chapters are devoted mainly to the following : (i) Walks, Paths, Cycles, Isomorphism, (ii) Matrix representation of Graphs and Digraphs; (iii) Connected graphs, connectivity, and complement; (iv) Bipartite graphs and Matching; (v) Eulerian and Hamiltonian graphs; (vi) Shortest path problems, Traveling Salesman’s Problems, Chinese Postman Problem; (vii) Tree, Binary tree, Breadth-First Search, Depth-First Search, Binary Search Tree, Tree traversals; (viii) Planar graphs, Platonic Graphs, Dual Graph, Line Graph; (ix) Graph Colouring-Vertex, Edge and Map.

**ABOUT THE AUTHORS**:

**Dr. B.C. Chakraborty** is a Professor of Pure Mathematics at Calcutta University. After passing his M.Sc. in Pure Mathematics with a first class in 1965 he joined the Pure Mathematics Dept. of Calcutta University as a lecturer in 1968 and continued there doing his research and teaching jobs till his retirement in 2007. In the meantime, he obtained his Ph.D. degree from Calcutta University in 1977 and became a professor in 1998. During his teaching career, he published many papers and presented them at several national and international conferences. He also guided successfully several students from India and Bangladesh to Ph.D. degrees. In 2000 he coauthored with his colleague Dr. M.K. Sen a book on Discrete Mathematics. He then became interested in Graph Theory and studied the subject intensively. The outcome is the present book on Graph Theory. After his retirement, he served the Departments of Mathematics of Bethune College and Dum Dum Motijheel College till 2019 as an invited professor.

**Dr. Sudip Chakraborty** is a Professor of Computer Science in the Department of Computer Science at Valdosta State University, USA, which he joined in 2008 as an Assistant Professor. His educational background includes B.Sc. in Mathematics from St. Xavier’s College, Kolkata, in 1997 and M.Sc. in Pure Mathematics from the University of Calcutta in 1999. He then changed his area of study to computer science and completed his M.Tech. in Computer Science from Indian Statistical Institute, Kolkata, in 2001. After a brief stint as a CSIR Senior Research Fellow in the Machine Intelligence Unit at Indian Statistical Institute, he moved to USA and earned his Ph.D. in Computer Science from Colorado State University in 2008. Dr. Chakraborty’s research focuses on cybersecurity and he has published several articles in international journals and conferences on various topics that include trust modeling, access control, cloud security, privacy, and cyberethics. His teaching involves a wide array of courses on programming languages, operating systems, databases, cybersecurity, ethics, and math-oriented courses like discrete mathematics and data structures. Though he teaches primarily computer science courses, he also taught introductory courses on algebra, trigonometry, and statistics. He enjoys connecting computer science concepts to their mathematical foundations. Contributing to a book on graph theory is especially exciting for him as he could discuss some of the many applications of graph theory in computer science.