Discrete Mathematics: Graph Algorithms, Algebraic Structures, Coding Theory, and Cryptography

• Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed.
• Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions.
• Provides an introduction to linear codes including cyclic codes.

Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a given
positive integer is prime or not in polynomial time is presented- the first time in a textbook.

Two distinguished features of the book are:

• Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described.
• Answers to all even-numbered exercises in all the chapters are given.