Introduction to Combinatorics and Graph Theory - Rama, R; - Prospero Internet Bookshop

Introduction to Combinatorics and Graph Theory
 
Product details:

ISBN13:9783031742514
ISBN10:3031742516
Binding:Hardback
No. of pages:504 pages
Size:240x168 mm
Language:English
Illustrations: Approx. 505 p.
700
Category:

Introduction to Combinatorics and Graph Theory

 
Edition number: 2025
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
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EUR 85.59
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  Piece(s)

 
Short description:

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.

Long description:

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.

Table of Contents:

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.