Introduction to Combinatorics and Graph Theory
Springer International Publishing (Verlag)
978-3-031-74251-4 (ISBN)
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The book covers all the basics of both the topics. The topics are sequenced in such a manner that there is a flow in understanding the advances. The first and second chapters cover all the basic methods and tools for counting. Chapter 3 is on binomial theorem and binomial identities. Topics such as partitions, permutations on multisets, generating functions, recurrence relation, principle of inclusion exclusion, repeated counting, partially ordered sets and Mobius inversion, Polya's counting are covered in different chapters. Some basic chapters have some worked-out exercise. Information on Catalan numbers, Eulerian Numbers, Narayana Numbers, and Schroder Number are given in a chapter. The topic on "discrete probability" covers the connection between counting techniques and probability theory.
There second part of the book covers topics in graph theory such as basics of graphs, trees,bipartite graphs, matching , planar graphs, Euler and Hamilton graphs, graph coloring, Ramsey theory, spectral properties, and some graph algorithms.Adequate exercise and examples are provided so as to enhance the reader's interest and understanding. Some interesting concepts like high hamiltonicity, power of graphs, domination, and matrix tree theorem are introduced.
Dr. R Rama holds a Ph.D. degree in Mathematics. She has over 32 years of teaching and research experience and has taught students at graduate and master's levels at IIT Madras since 1995. She has guided eight Ph.D. students. At present, Dr. Rama is Girija Vaidyanathan Chair Professor at the Department of Mathematics, IIT Madras.She has co-authored a book on "Formal Languages and Automata Theory" that is widely used in Indian Universities either as textbook or as reference book, published by Pearson education in two languages, English and Chinese. 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 theoretical computer science.
Basics of Counting.- Induction and Pigeon Hole Principle.- Binomial Theorem and Binomial Identities Partitions.- Permutations.- Combinations and Cycles.- Generating Functions.- Recurrence Relations.- Inclusion Exclusion Principle.- Partial Order and Lattices.- Polya's Theory.- More on Counting.- Discrete Probability.- Basic Concepts.- Paths Connectedness.- Trees.- Connectivity.- Eulerian and Hamiltonian Graphs.- Planar Graphs.- Independent Sets.- Coverings and Matchings.- Graph Coloring.- Ramsey Numbers and Ramsey Graphs.- Spectral Properties of Graphs.- Directed Graphs and Graph Algorithms.
| Erscheint lt. Verlag | 24.2.2025 |
|---|---|
| Zusatzinfo | Approx. 505 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| Schlagworte | binomial identities • Binomial Theorem • Discrete Probability • Eulerian numbers • Generating functions • Narayana numbers • Partitions • Permutations on multisets • Polya's Counting • Recurrence relation • Schroder Number |
| ISBN-10 | 3-031-74251-6 / 3031742516 |
| ISBN-13 | 978-3-031-74251-4 / 9783031742514 |
| Zustand | Neuware |
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