Graph Theory

Master the Nuts and Bolts of Graph Theory: the Heart of Communication and Transportation Networks, Internet, GPS, ...
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  • Lectures 74
  • Length 6 hours
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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About This Course

Published 5/2016 English

Course Description

What is this course about?

Graph Theory is an advanced topic in Mathematics. On a university level, this topic is taken by senior students majoring in Mathematics or Computer Science; however, this course will offer you the opportunity to obtain a solid foundation in Graph Theory in a very short period of time, AND without requiring you to have any advanced Mathematical background.

You don’t need to know complex Mathematical statements, or rules, but ALL you need to know is simple mathematical operations like addition and multiplication. The course is designed to be understood by an 11th grader since the structure of the course starts with the very basic idea of how to create a Graph, and with each step the ideas get more and more complex. The structure of the course goes as following starting with the first section:

  1. Graphs: In this section you will learn basic definitions like Vertex, Edge, Distance,                            Contentedness, and many other concepts that are the alphabet of Graph                          Theory. 
  2. Types of Graphs: In this section you will learn a variety of different Graphs, and their                       properties. 
  3. Graph Operations: In this section you will learn different operations and different                             methods in making new Graphs. 
  4. Graph Coloring: in this section you will learn Graph Coloring and many related                                 concepts. 
  5. Paths: in this lecture you will learn Euler and Hamiltonian Paths and Circuits, and                             many other concepts in that area. 
  6. Trees: In this section you will learn about Trees, Tree Traversals, Binary Expression                         Trees and some more. 
  7. And Graph Match: In this section you will about Graph Match and Graph Cover. 


How are the concepts delivered?

Each lecture is devoted to explaining a concept or multiples concepts related to the topic of that section. There are example(s) after the explanation(s) so you understand the material more. The course is taught in plain English, away from cloudy, complicated mathematical jargons and that is to help the student learn the material rather than getting stuck with fancy words.


How to learn better?

Take notes and repeat the lectures to comprehend the concepts more. Also, there are quizzes every 3-5 lectures so you can test what you have learned and go over something if needed. 

What are the requirements?

  • To know elementary operations like addition and multiplication

What am I going to get from this course?

  • Master fundamental concepts in Graph Theory
  • Get to know a wide range of different Graphs, and their properties.
  • Be able to preform Elementary, Advanced Operations on Graphs to produce a new Graph
  • Understand Graph Coloring.
  • Understand Eulerian and Hamiltonian paths and circuits. And many related topics to Paths.
  • Know how to turn a Graph into a Matrix and vice versa.
  • Obtain a solid foundation in Trees, Tree Traversals, and Expression Trees.
  • Have a good understanding of Graph Match.

What is the target audience?

  • Mathematics or Computer Science students
  • Anyone interested in learning advanced Mathematics in an easy way

What you get with this course?

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30 day money back guarantee.

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Lifetime access.

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Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Introduction
Preview
02:04
Section 1: Graphs
06:29

In this lecture we will define Graphs, Vertices, Edges, Degree of a Vertex, Degree Sequence, Graph Order, and Graph Size. And we will get to know the importance of Graphs. 

03:39

In this lecture we will get to know Subgraphs, and we will define Vertex Set and Edge Set. 

Quiz
4 questions
03:25

In this lecture we will explore Graph Isomorphism and its conditions. 

Graph Automorphism
03:52
Quiz
3 questions
03:45

In this lecture we will talk about Complement Graphs, and what it means for Vertices to be adjacent.   

01:48

In this lecture we will talk about what it means for two Vertices to be connected by more than one Edge. 

Quiz
4 questions
11:56

In this lecture we will talk about Adjacency Matrix and Incidence Matrix.

Quiz
3 questions
08:08

In this lecture we will define Walks, Trails, and Paths, and the difference between them. Also, we will talk about Self Avoiding Paths (SAP). 

05:49

In this lecture we will talk about how Distance is measured in Graphs. 

06:46

In this lecture we will talk about Graph Connectedness, Cut Edge, Cut Vertex, and Separating Sets.  

Quiz
6 questions
Menger's theorem
08:22
Sum of Degrees of Vertices Theorem
03:38
Section 2: Graph Types
Introduction
Preview
00:59
03:49

In this lecture we will define Null, Trivial, Simple Graphs, Loops, and Parallel Edges.

Regular, Complete and Weighted Graphs
03:01
07:52

In this lecture we will define Directed Graphs, Indegree, Outdgree, a Source, and a Sink, and we will learn how we can do Adjacency Matrix for a Directed Graph. We will also talk about Undirected, and Mixed Graphs.

Quiz
4 questions
08:13

In this lecture we will learn the difference between Cycle Graphs, and a Cycle in a Graph. We will also define Girth of a Graph, Path Graphs, Wheel Graphs, and Lollipop Graphs. 

Planar, Cubic and Random Graphs
04:05
05:33

In this lecture we will talk about Ladder and Prism Graphs, and how we can count the number of the Edges in each.  

05:43

In this lecture we will define Web and Signed Graphs, and we will get to know a psychologist's contribution to Graph Theory. 

Quiz
7 questions
Peterson Graph
00:55
Bipartite Graphs
03:31
03:11

The illustrations shown in this lecture are NOT owned by the instructor of this course. To reach the website containing the illustrations, follow this link : https://www.learner.org/interactives/geometry/platonic.html

Section 3: Graph Operations
Introduction
Preview
02:19
Vertex Addition and Deletion
02:30
Edge Addition and Deletion
02:27
Vertex Contraction and Edge Contraction
05:06
Quiz
2 questions
Graph Minor and Graph Transpose
03:33
05:43

In this lecture we will talk about Line Graphs which, and the process of creating them. 

04:57

In this lecture we will talk about the process of creating a Dual Graph from another Graph. 

03:26

In this lecture, we will talk about how to find the k^th Power of a Graph. 

Y - Δ Transform
02:26
Quiz
5 questions
06:46

In the lecture we will talk about the process of Joining and the steps that go into the Cartesian Product of two Graphs.  

In Cartesian Product of two graphs, I mention the word "multiply" which in this context means "Product" or "Cartesian Product".  

Hajós Construction
04:09
04:18

In this lecture we will talk about how we can create a new Graph by Union and Intersection of two Graphs. 

Series - Parallel Composition
02:51
Quiz
4 questions
Section 4: Graph Coloring
Introduction
Preview
01:04
07:26

In this lecture we will define Vertex Coloring, Chromatic Number, k-Colorable Graphs, and Independent Sets. 

Edge Coloring
03:49
Quiz
3 questions
05:31

In this lecture we will define Chromatic Polynomials and show you how to use the software to find the Chromatic Polynomial of any Graph. Here is the link to Bob Weaver's website: http://www.mtholyoke.edu/~bweaver/vita/software.htm

Total and List Coloring
07:03
Exact and Fractional Coloring
03:59
Rainbow Coloring
03:11
04:14

In this lecture we will talk about Vizing's Theorem and Maximum Degree. 

Four Color Theorem
02:23
Section 5: Paths
Introduction
Preview
01:17
01:43

In this lecture we will talk about what triggered Graph Theory. 

08:20

In this lecture we will define Euler Paths and Euler Circuits, and we will see why there isn't a solution to the Königsberg Bridge Problem. 

05:14

In this lecture we will talk about Fleury's way of finding an Euler Path or Circuit. 

Hierholzer's Algorithm
10:48
Quiz
3 questions
05:33

In this lecture we will define Hamiltonian Paths and Circuits. 

01:33

In this lecture we will explore decomposing a Graph based on the Hamiltonian Circuits in it. 

Ore's Theorem
04:28
Dirac's Theorem
03:30
Quiz
3 questions
13:59

In this lecture we will see how we can find the shortest path in a Graph using Dijkstra's Algorithm. 

Five Room Puzzle
04:22
Knight's Tour
03:25
Section 6: Trees
Introduction
Preview
00:59
05:26

In this lecture we will define Trees, their properties, their importance in Computer Science, and how we can count them using Cayley's Formula. 

03:49

In this lecture we will talk about Star Trees, Caterpillar Trees, Lobster Trees, and Banana Trees. 

06:24

In this lecture we will define Rooted Trees, Out Tree, In Tree, Parent, Child, Sibling, Ancestor, Descendant, Uncle, Leaf, Internal and External Vertices, Subtree, Levels, Height, and Depth. 

05:36

In this lecture, we will talk about different ways we can represent a Tree visually. 

Quiz
5 questions
07:50

In this lecture we will talk about Binary Trees, and its different types (Proper, Perfect, Complete, Infinite Complete, and Balanced Binary Trees). 

Spanning Trees
04:44
Quiz
4 questions
06:36

In this lecture you will learn how to convert an Algebraic or Boolean expression into a Tree and vice versa. 

14:02

In this lecture we will talk about Preorder, Inorder, Postorder, and Levelorder Tree Traversals. To practice more, go to below website and you will find numerous practice examples at the very end of the page. 

http://algoviz.org/OpenDSA/Books/OpenDSA/html/BinaryTreeTraversal.html

Quiz
3 questions
Forests
01:36
Section 7: Graph Match
Introduction
Preview
00:32
06:50

In this lecture we will get to know Matching, Maximum and Maximal Matching, Perfect Matching, and Near Perfect Matching. 

Hosoya Index
Preview
02:57
02:30

In this lecture, beside talking about Berge's Lemma, we will talk about Augmenting Paths, and Alternating Paths. 

Vertex and Edge Cover
03:53
01:22

In this lecture we will see the relationship between Matching and Vertex Cover for Bipartite Graphs. 

Quiz
5 questions

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Instructor Biography

Miran Fattah, B.S. in Mathematics & Geophysics

Fattah has B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States so to return back to his home country and teach. 

He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and his aim is to deliver the concepts in an easy and direct way so as to make the learning process fast for everyone.

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