Graph Theory and Combinatorics 10CS42
Graph Theory and combinatorics 10CS42 GRAPH THEORY AND COMBINATORICS Sub code: 10CS42 IA Marks: 25 Hours/Week: 04 Exam hours: 03 Total hours: 52 Exam marks: 100 UNIT-1 Introduction to Graph Theory: Definition and Examples Subgraphs Complements, and Graph Isomorphism Vertex Degree, Euler Trails and Circuits. UNIT-2 Introduction the Graph Theory Contd.: Planner Graphs, Hamiloton Paths and Cycles, Graph Colouring and Chromatic Polynomials. UNIT-3 Trees : definition, properties and examples, rooted trees, trees and sorting, weighted trees and prefix codes UNIT-4 Optimization and Matching: Dijkstra‘s Shortest Path Algorithm, Minimal Spanning Trees – The algorithms of Kruskal and Prim, Transport Networks – Max-flow, Min-cut Theorem, Matching Theory UNIT-5 Fundamental Principles of Counting: The Rules of Sum and Product, Permutations, Combinations – The Binomial Theorem, Combinations with Repetition, The Catalon Numbers UNIT-6 The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion, Generalizations of the Principle, Derangements – Nothing is in its Right Place, Rook Polynomials UNIT-7 Generating Functions: Introductory Examples, Definition and Examples – Calculational Techniques, Partitions of Integers, The Exponential Generating Function, The Summation Operator UNIT-8 Recurrence Relations: First Order Linear Recurrence Relation, The Second Order Linear Homogeneous Recurrence Relation with Constant Coefficients, The Non-homogeneous Recurrence Relation, The Method of Generating Functions Dept of CSE, SJBIT 1 Graph Theory and combinatorics 10CS42 INDEX Sl.No. Topics Page No. 1 Unit 1 - Introduction 1 -34 2 Unit 2 - Planar Graphs 35-67 3 Unit 3 – trees 68-80 4 Unit 4 - Optimization and Matching 81-96 5 Unit 5 - Fundamental Principles of Counting 97-134 6 Unit 6 - The Principle of Inclusion and Exclusion 135-150 7 Unit 7 – Generating Functions 151-187 8 Unit 8 - Recurrence Relations 188 - 213 Dept of CSE, SJBIT 2 Graph Theory and combinatorics 10CS42 UNIT 1 INTRODUCTION This topic is about a branch of discrete mathematics called graph theory.
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