Hey!! As per your demand here I am providing you syllabus of the Graph Theory and Combinatorics syllabus for CS 4 Sem of VTU

Part A

Unit-1
Introduction to Graph Theory
Definitions and Examples, Subgraphs, Complements, and Graph Isomorphism, Vertex Degree, Euler Trails and Circuits

Unit-2
Introduction to Graph Theory contd
Planar Graphs, Hamilton Paths and Cycles, Graph Colouring, and Chromatic Polynomials

Unit-3
Trees
Definitions, Properties, and Examples, Routed 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

Part B

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