Tutorialspoint
Subscription Includes
 07:27:58 of High Quality Videos
 97  Lectures
 Full Lifetime Access
 Certificate on Completion
$ 132   9.99

Graph Theory

Simply Easy Learning

Created by Arnab Chakraborty, Last Updated 05-Sep-2019, Language:English

Description

This tutorial offers an introduction to the fundamentals of graph theory. It is in a very reader-friendly tutorial style. It covers the types of graphs, their properties, different terminologies, trees, graph traversability, the concepts of graph colouring, different graph representation techniques, concept of algorithms and different graph theory based algorithms.

Audience

This tutorial has been designed for students who want to learn the basics and algorithms of Graph Theory. Graph Theory has a wide range of applications in engineering and hence, this tutorial will be quite useful for readers who are into Language Processing or Computer Networks, physical sciences and numerous other fields.

Course Content

  • Graph Theory 1 Lectures 00:01:48

    • Graph Theory And It's Application - Getting Started

      Preview
      00:01:48
  • Graph Theory Introduction 3 Lectures 00:09:16

    • Definition of Data Structure

      00:01:05

    • Classification of Data Structure

      00:02:48

    • Definition of Graph and Its Applications

      00:05:23
  • Graph Theory Fundamentals 7 Lectures 00:19:05

    • Graph - Degree of a Vertex

      00:03:25

    • Graph - In-Degree and Out-Degree

      00:03:35

    • Graph - Theorem on Degree of Vertices

      00:03:08

    • Graph - Articulation Point Definition

      00:03:02

    • Graph - Exercise on Articulation Point

      00:02:19

    • Graph - Adjacency and Adjacent Vertices

      00:02:05

    • Graph - Multigraph

      00:01:31
  • Graph Basic Properties 2 Lectures 00:04:07

    • Graph - Eccentricity of a Vertex

      00:01:41

    • Graph - Radius and Diameter

      00:02:26
  • Types of Graph 12 Lectures 00:33:16

    • Graph Types - Introduction

      Preview
      00:02:54

    • Graph Types - Connected and Disconnected

      00:02:13

    • Graph Types - Directed and Undirected Graph

      00:03:43

    • Graph Types - Regular and Complete

      00:03:56

    • Graph Types - Regular Graph

      00:01:39

    • Graph Types - Complete Graph

      00:03:26

    • Graph Types - Sub-Graph

      00:02:21

    • Graph Types - Bipartite Graph

      00:05:21

    • Graph Types - Complement of a Graph

      00:01:50

    • Undirected Graph - GATE Exercise 1

      00:01:49

    • Undirected Graph - GATE Exercise 2

      00:02:35

    • Undirected Graph - GATE Exercise 3

      00:01:29
  • Trees 6 Lectures 00:19:57

    • Spanning Trees

      Preview
      00:02:34

    • Kirchhoff’s Matrix Tree Theorem

      00:04:43

    • Minimum Cost Spanning Trees

      00:03:27

    • Circuit Rank

      00:01:57

    • Minimum Spanning Tree - GATE Exercise 1

      00:03:26

    • Minimum Spanning Tree - GATE Exercise 2

      00:03:50
  • Graph Coloring 3 Lectures 00:23:00

    • Vertex Coloring and Chromatic Number

      00:02:34

    • Graph Coloring Problem

      00:11:02

    • Graph Coloring Algorithm

      00:09:24
  • Graph Isomorphic 2 Lectures 00:09:17

    • Isomorphic Graphs

      00:06:58

    • Homomorphism

      00:02:19
  • Graph Traversibility 7 Lectures 00:41:00

    • Graph Traversals Introduction

      Preview
      00:02:29

    • Graph Traversability Euler’s Path And Euler’s Circuit

      00:02:58

    • Graph Traversability Hamiltonian Graph and Hamiltonian Cycle

      00:03:46

    • Travelling Salesman Problem

      00:07:38

    • Travelling Salesman Problem Example

      00:09:13

    • Problem on Hamiltonian Cycles

      00:03:46

    • Algorithm For Hamiltonian Cycles

      00:11:10
  • Graph Representation Techniques 7 Lectures 00:29:25

    • Graph Representation Techniques Introduction

      00:02:06

    • Graph Representation Techniques Adjacency Matrix

      00:03:26

    • Graph Representation Techniques Incidence Matrix

      00:05:27

    • Graph Representation Techniques Sequential Representation

      00:04:43

    • Graph Representation Techniques Adjacency List

      00:05:24

    • Graph Representation Techniques Orthogonal List

      00:03:07

    • Graph Representation Techniques Adjacency Multi List

      00:05:12
  • Algorithm and Complexity Analysis 8 Lectures 00:30:14

    • What Is an Algorithm?

      00:03:22

    • Space and Time Complexity of an Algorithm

      00:06:39

    • Time Complexity Big-Oh Notation

      00:04:04

    • Time Complexity Big-Omega Notation

      Preview
      00:03:59

    • Time Complexity Big-Theta Notation

      00:04:42

    • Asymptotic Notations - GATE Exercise 1

      00:01:54

    • Asymptotic Notations - GATE Exercise 2

      00:02:34

    • Exercise on Time Complexity

      00:03:00
  • Algorithm and Classification 13 Lectures 00:55:06

    • Algorithm Classification Introduction

      00:03:08

    • Algorithm Classification Simple Recursive Algorithm

      00:03:12

    • Definition of Recursion

      00:09:01

    • Recursion - GATE Exercise 1

      00:03:01

    • Recursion - GATE Exercise 2

      00:04:10

    • Algorithm Classification Back Tracking Algorithm

      00:04:17

    • Algorithm Classification Divide and Conquer

      00:02:17

    • Algorithm Classification Dynamic Programming

      00:03:14

    • Algorithm Classification Greedy Algorithm

      00:06:25

    • A Sample Greedy Algorithm

      Preview
      00:05:43

    • Algorithm Classification Branch and Bound

      00:05:09

    • Algorithm Classification Brute Force

      00:03:41

    • Algorithm Classification Randomized Algorithm

      00:01:48
  • Graph Theory Algorithm 26 Lectures 02:52:27

    • Depth First Search Algorithm on Undirected Graph

      00:04:36

    • Depth First Search Algorithm on Undirected Graph Example

      00:08:43

    • Breadth First Search Algorithm

      00:05:15

    • Breadth First Search Algorithm Example

      00:06:44

    • Algorithm To Calculate Number of Components of a Graph

      00:06:12

    • Comparison and Complexity of DFS and BFS Algorithms

      00:06:20

    • Exercise on BFS Algorithm

      00:07:28

    • Prim’s Algorithm to Find Minimum Spanning Tree

      00:05:21

    • Prim’s Algorithm to Find Minimum Spanning Tree Example

      00:05:14

    • Kruskal’s Algorithm to Find Minimum Spanning Tree

      00:05:38

    • Kruskal’s Algorithm to Find Minimum Spanning Tree Example

      00:06:54

    • Comparison and Complexity of Prim’s and Kruskal’s Algorithms

      00:09:08

    • Exercise on Prim’s Algorithm

      00:07:06

    • Kruskal’s Algorithm - GATE Exercise 1

      00:03:59

    • Kruskal’s Algorithm - GATE Exercise 2

      00:03:38

    • Floyd’s Algorithm to Find Cost Matrix

      00:04:49

    • Floyd’s Algorithm To Find Cost Matrix Example

      00:05:33

    • Warshall’s Algorithm to Find Path Matrix

      00:06:06

    • Warshall’s Algorithm to Find Path Matrix Example

      00:04:38

    • Dijkstra’s Algorithm For All Pair Shortest Path

      Preview
      00:06:52

    • Dijkstra’s Algorithm For All Pair Shortest Path Example

      00:10:23

    • Ford-Fulkerson Algorithm For Maximum Flow Problem

      00:09:04

    • Ford-Fulkerson Algorithm For Maximum Flow Problem Example

      00:13:12

    • Ford-Fulkerson Algorithm For Maximum Flow Problem Complexity

      00:02:25

    • Bellman Ford Algorithm to Calculate Shortest Paths

      00:06:12

    • Bellman Ford Algorithm to Calculate Shortest Paths Example

      00:10:57

Arnab Chakraborty

Corporate Trainer

Prof. Arnab Chakraborty is a Calcutta University alumnus with B.Sc. in Physics Hons with Gold medalist, B. Tech and M. Tech in Computer Science and Engineering has twenty-three+ years of academic teaching experience in different universities, colleges and eleven+ years of corporate training experiences for 150+ companies and trained 50,000+ professionals. He has also completed MBA from Vidyasagar University with dual specialization in Human Resource Management and Marketing Management. He is NLP and PMP trained, Global DMAIC Six Sigma Master Black Belt certified by IQF, USA. He is certified by ISA, USA on "Control and Automation System". He is also Global ITIL V3 Foundation certified as awarded by APMG, UK. Qualified for Accredited Management Teacher by AIMA. He is also empaneled trainer for HP, Accenture, IBM etc.