Topics in Combinatorics and Graph Theory / by R. Rama.

Format:

Book

Author/Creator:

Rama, R., Author.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Graph theory.

Discrete mathematics.

Probabilities.

Graph Theory.

Discrete Mathematics.

Probability Theory.

Graph Theory in Probability.

Local Subjects:

Graph Theory.

Discrete Mathematics.

Probability Theory.

Graph Theory in Probability.

Physical Description:

1 online resource (X, 454 p. 257 illus., 1 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-74252-4

OCLC:

1522508967