Topics in Combinatorics and Graph Theory

This book "Topics in Combinatorics and Graph Theory" covers all the basics of both topics that are sequenced to flow the understanding of advances. Mathematical concepts are explained with examples and explanations are provided at appropriate places to enhance readability and ease of understanding. The examples and exercises include problems of varying difficulty. Each topic in the book has been presented in a comprehensive manner so as to cross over to some advanced concepts gradually. Some relevant applications have also been presented for the interest of academic researchers and industry. The content of the book is good enough for self-study for students at UG and PG level. Some of the salient features are: The book presents concepts in a concise and clear manner. Results that are fundamental to understand enumerative combinatorics and graph structures are given and proved. The book has adequate basics needed to learn/teach the content. The readability is enhanced via examples at appropriate places. Every Chapter has doable exercise. Each chapter includes a good introduction and concludes with notes. Increased coverage of topics in both combinatorics and graph theory. Some standard algorithms on these topics are included. Contents Part I: Combinatorics 1 Basics of Counting 2 Induction and Pigeon Hole Principle 3 Binomial Theorem and Binomial Identities 4 Partitions 5 Permutations, Combinations and Cycles 6 Generating Functions 7 Recurrence Relations 8 Inclusion Exclusion Principle 9 Partial Order and Lattices 10 Polya's Theory 11 More on Counting 12 Discrete Probability Part II: Graph Theory 13 Basic Concepts 14 Paths Connectedness 15 Trees 16 Connectivity 17 Eulerian and Hamiltonian Graphs 18 Planar Graphs 19 Independent Sets, Coverings and Matchings 20 Graph Coloring 21 Ramsey Numbers and Ramsey Graphs 22 Spectral Properties of Graphs 23 Directed Graphs and Graph Algorithms, Bibliography, Index.…