Discrete Mathematics And Graph Theory

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This comprehensive and self-contained text provides a thorough understanding of the concepts and applications of discrete mathematics and graph theory. It is written in such a manner that beginners can develop an interest in the subject. Besides providing the essentials of theory, the book helps develop problem-solving techniques and sharpens the skill of thinking logically.

The book is organized in two parts. The first part on discrete mathematics covers a wide range of topics such as predicate logic, recurrences, generating function, combinatorics, partially ordered sets, lattices, Boolean algebra, finite state machines, finite fields, elementary number theory and discrete probability. The second part on graph theory covers planarity, colouring and partitioning, directed and algebraic graphs.

In the Second Edition, more exercises with answers have been added in various chapters. Besides, an appendix on languages has also been included at the end of the book.

The book is intended to serve as a textbook for undergraduate engineering students of computer science and engineering, information communication technology (ICT), and undergraduate and postgraduate students of mathematics. It will also be useful for undergraduate and postgraduate students of computer applications.

KEY FEATURES

Provides algorithms and flow charts to explain several concepts.
Gives a large number of examples to illustrate the concepts discussed.
Includes many worked-out problems to enhance the students grasp of the subject.
Provides exercises with answers to strengthen the students problem-solving ability.

AUDIENCE

Undergraduate Engineering students of Computer Science and Engineering, Information communication technology (ICT)
Undergraduate and Postgraduate students of Mathematics.
Undergraduate and Postgraduate students of Computer Applications.

Preface

Part I: DISCRETE MATHEMATICS

1. Preliminary Notations

2. Fundamentals of Logic

3. Recurrences and Integer Functions

4. Counting Techniques

5. Algebraic Systems

6. Partially-Ordered Sets

7. Lattices

8. Boolean Algebras

9. Finite Machines

10. Finite Fields

11. Elementary Number Theory

12. Discrete Probability

Part II: GRAPH THEORY

13. Preliminary Concepts

14. Planarity, Colouring and Partitioning

15. Some Algebraic Aspects of Graphs

16. Directed Graphs

Appendix: Languages Bibliography Glossary Index