uLektz Skills

Learning Path

Non-Linear: Random Order

About the Course

Course Description

This course deals with some basic concepts in graph theory like properties of Tress, connectivity & planarity, Matrices. This course is designed with Colouring and directed graph, Permutations and combinations and Generating functions

Objectives

1.Will familiarize about Graphs and Isomorphism

2.Will demonstrate Block Matrices, Colouring and directed graph

3.Will develop knowledge in Generating functions

Prerequisite

There is no particular prerequisite to learn Graph Theory and Applications, you will be able to do very well, if you have these basic skills:

1. Basic Knowledge in programming

2. Good Computer Knowledge

3. Good communication skills

4. Good Knowledge Maths and Analytics

Course Study Materials

Module 1: Introduction

1.1 Graphs and Isomorphism
1.2 Sub graphs and Connectedness
1.3 Components, Euler graphs, Hamiltonian paths and circuits and Trees
Introduction - Assessment 10 Questions

Module 2: Tress, connectivity & planarity

2.1 Spanning trees, Fundamental circuits, Spanning trees in a weighted graph and Cut sets
2.2 Connectivity and separability, Network flows and 1-Isomorphism
2.3 2-Isomorphism, Combinational and geometric graphs and Planer graphs
Tress, connectivity & planarity - Assessment 10 Questions

Module 3: Matrices, Colouring and directed graph

3.1 Chromatic number, Chromatic partitioning and Chromatic polynomial
3.2 Matching, Covering, Four color problem and Directed graphs
3.3 Digraphs and binary relations, Directed paths and connectedness and Euler graphs
Matrices, Colouring and directed graph - Assessment 10 Questions

Module 4: Permutations and combinations

4.1 Fundamental principles of counting and Permutations and combinations
4.2 Binomial theorem, Combinations with repetition, Combinatorial numbers, Principle of inclusion and exclusion, Derangements and Arrangements with forbidden positions.
Permutations and combinations - Assessment 10 Questions

Module 5: Generating functions

5.1 Generating functions, Partitions of integers, Exponential generating function and Summation operator
5.2 Recurrence relations, First order and second order, Non-homogeneous recurrence relations and Method of generating functions.
Generating functions - Assessment 10 Questions

Final Assessment

Final Assessment 20 Questions

The certificate issued for the Course will have

Student's Name
Photograph
Course Title
Certificate Number
Date of Course Completion
Name(s) and Logo(s) of the Certifying Bodies

Only the e-certificate will be made available. No Hard copies. The certificates issued by The Academic Council of uLektz. can be e-verifiable at www.ulektzskills.com/verify.

Students will be assessed both at the end of each module and at the end of the Course.
Students scoring a minimum of 50% in the assessments are considered for Certifications