Visvesvaraya Technological University, Karnataka, Computer Engineering Semester 4, Graph Theory and Combinatorics Syllabus

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Unit - 1 Introduction to Graph Theory

1.1 Graph Theory

1.2 Types of Graphs

1.3 Complement of graph

1.4 Graph isomorphism

1.5 Vertex Degree

Unit - 2 Introduction to Graph Theory

2.1 Planar Graph

2.2 Hamiltonian Path and Cycle

2.3 Graph Colouring

2.4 Chromatic Polynomial

Unit - 3 Trees

3.1 Definition and properties

3.2 Forest

3.3 Properties of Trees

3.4 Rooted Trees

3.5 Height of the tree

3.6 Sorting

3.7 Weighted tree

3.8 Prefix Codes

Unit - 4 Optimization and Matching

4.1 Dijkstra’s Shortest Path Algorithm

4.2 Minimum Spanning Tree

4.3 Kruskal’s Algorithm

4.4 Prim’s Algorithm

4.5 Transport Networks

4.6 Matching Theory

Unit - 5 Fundamental Principles of Counting

5.1 The Rules of Sum and Product

5.2 Permutations

5.3 Combinations

5.4 The Binomial Theorem

5.5 Combinations with Repetition

5.6 Catalan numbers

Unit - 6 The Principle of Inclusion and Exclusion

6.1 The Principle of Inclusion and Exclusion

6.2 Derangements – Nothing is in its Right Place

6.3 Rook Polynomial

Unit - 7 Generating Functions

7.1 General generating function

7.2 Application of the general generating function of a series Calculating combinations

7.3 Exponential generating function

7.4 Partitions of Integers

7.5 Exponential Generating Function

7.6 Summation Operator

Unit - 8 Recurrence Relations

8.1 Recurrence Relations

8.2 Linear Recurrence Relations

8.3 Second Order Linear Homogeneous Recurrence Relation with Constant Coefficients

8.4 Nonhomogeneous Recurrence relation and particular solution

8.5 Generating Functions

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Other Subjects of Semester-2
Microprocessors
Computer organization
Unix and shell programming
Engineering mathematics - iv
Design and analysis of algorithms
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