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
  
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  00:01:48
Graph Theory Introduction

3 Lectures 00:09:16
- Definition of Data Structure
  
  Preview
  
  00:01:05
- Classification of Data Structure
  
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  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
  
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  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
  
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  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
  
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  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
  
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  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
  
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  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
  
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  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 Gold medalist, B. Tech and M. Tech in Computer Science and Engineering has twenty-six+ years of academic teaching experience in different universities, colleges and thirteen+ years of corporate training experiences for 170+ 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 "Global ITIL V3 Foundation" certified as awarded by APMG (UK). Qualified for "Accredited Management Teacher" by AIMA (India). "Star Python" Global Certified from Star Certification (USA). "Certified Scrum Master (CSM)" Global Certification from Scrum Alliance (USA). He is also empaneled trainer for multiple corporates, e.g. HP, Accenture, IBM etc