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Topics in combinatorics and graph theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topics in combinatorics and graph theoryby R. Rama.
Author:	Rama, R.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	x, 454 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Combinatorial analysis.
Online resource:	https://doi.org/10.1007/978-3-031-74252-1
ISBN:	9783031742521$q(electronic bk.)

Topics in combinatorics and graph theory
Rama, R.

Topics in combinatorics and graph theory[electronic resource] /by R. Rama. - Cham :Springer Nature Switzerland :2025. - x, 454 p. :ill. (some col.), digital ;24 cm.

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.

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.

ISBN: 9783031742521$q(electronic bk.)

Standard No.: 10.1007/978-3-031-74252-1doiSubjects--Topical Terms:

182280
Combinatorial analysis.

LC Class. No.: QA164

Dewey Class. No.: 511.6

Topics in combinatorics and graph theory
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245 1 0 $a Topics in combinatorics and graph theory $h [electronic resource] / $c by R. Rama.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a x, 454 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Combinatorial analysis. $3 182280
650 0 $a Graph theory. $3 181880
650 1 4 $a Graph Theory. $3 522732
650 2 4 $a Discrete Mathematics. $3 524738
650 2 4 $a Probability Theory. $3 913371
650 2 4 $a Graph Theory in Probability. $3 913380
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