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Learning Path

Linear: Sequential 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


1.Will familiarize about Graphs and Isomorphism

2.Will demonstrate Block Matrices, Colouring and directed graph

3.Will develop knowledge in Generating functions


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 the student's Name, Photograph, Course Title, Certificate number, Date of course completion and the name(s) and logo(s) of the Certifying Bodies. Only the e-certificate will be made available. No Hard copies. The certificates issued by uLektz Learning Solutions Pvt. Ltd. can be e-verifiable at www.ulektzskills.com/verify.

  • Students are required to take online assessments with eProctoring.
  • 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
  • 80 hours Learning Content
  • 100% online Courses
  • English Language
  • Certifications


Registration opens on 04-02-2019


Your registration details are under review. It should take about 1 to 2 working days. Once approved you will be notified by email and then you should be able to access the course.

Course Approved

Approval Pending - In-Progress

Course access details will be shared within 24 hours.
For help contact: support@ulektz.com

Course Enrollment


Course starts on 11-05-2021


You have completed 6 hours of learning for 20-01-2022. You can continue learning starting 21-01-2022.


This course can only be taken in sequential order.


You have completed the course. You will be notified by email once the certificate is generated.


Are you sure want to enroll this course?.



S.no Date Title Reason

Result Summary

Graph Theory and Applications