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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.
Dr. R Rama holds a PhD degree in Mathematics. She has over 32 years of teaching and research experience and has taught students at graduate and master's level at I IT Madras since 1995. She has guided eight Ph D students also. At present Dr. Rama is Girija Vaidhyanathan Chair Professor at the department of mathematics, I IT Madras. She has co-authored a book on "Formal Languages and Automata Theory", published by Pearson education in two languages, English and Chinese, that is widely used in Indian Universities. She has also edited volumes on research articles for international publishers. She has presented her research papers in several national and international conferences. Her major area of interest and research is Discrete Mathematics.
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
