Graph Theory
4.3 (12 ratings)
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Graph Theory

Master the Nuts and Bolts of Graph Theory: the Heart of Communication and Transportation Networks, Internet, GPS, ...
4.3 (12 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
185 students enrolled
Created by Miran Fattah
Last updated 3/2017
English
Current price: $10 Original price: $65 Discount: 85% off
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Includes:
  • 6 hours on-demand video
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I Learn?
  • 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.
View Curriculum
Requirements
  • To know elementary operations like addition and multiplication
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. 

Who is the target audience?
  • Mathematics or Computer Science students
  • Anyone interested in learning advanced Mathematics in an easy way
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Curriculum For This Course
Expand All 74 Lectures Collapse All 74 Lectures 05:45:51
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Introduction
1 Lecture 02:04
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Graphs
12 Lectures 01:08:26

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. 

Graphs
06:29

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

Subgraphs
03:39

Quiz
4 questions

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

Graph Isomorphism
03:25

Graph Automorphism
03:52

Quiz
3 questions

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

Complement Graph
03:45

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

Multigraphs
01:48

Quiz
4 questions

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

Matrix Representation
13:41

Quiz
3 questions

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

Walks, Trails and Paths
08:08

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

Distance
05:49

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

Connectedness
06:46

Quiz
6 questions

Menger's theorem
08:22

Sum of Degrees of Vertices Theorem
02:42
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Graph Types
11 Lectures 46:52

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

Null, Trivial, and Simple Graphs
03:49

Regular, Complete and Weighted Graphs
03:01

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.

Directed, Undirected and Mixed Graphs
07:52

Quiz
4 questions

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. 

Cycle, Path, Wheel and Lolipop Graphs
08:13

Planar, Cubic and Random Graphs
04:05

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

ladder and Prism Graphs
05:33

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

Web and Signed Graphs
05:43

Quiz
7 questions

Peterson Graph
00:55

Bipartite Graphs
03:31

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

Platonic Graphs
03:11
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Graph Operations
13 Lectures 50:31

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

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

Line Graphs
05:43

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

Dual Graphs
04:57

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

Graph Power
03:26

Y - Δ Transform
02:26

Quiz
5 questions

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".  

Graph Join and Graph Product
06:46

Hajós Construction
04:09

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

Graph Union and Graph Intersection
04:18

Series - Parallel Composition
02:51

Quiz
4 questions
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Graph Coloring
9 Lectures 38:40

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

Vertex Coloring
07:26

Edge Coloring
03:49

Quiz
3 questions

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

Chromatic Polynomial
05:31

Total and List Coloring
07:03

Exact and Fractional Coloring
03:59

Rainbow Coloring
03:11

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

Vizing's Theorem
04:14

Four Color Theorem
02:23
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Paths
12 Lectures 01:04:12

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

The Königsberg Bridge Problem
01:43

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. 

Euler Paths and Circuits
08:20

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

Fleury’s Algorithm
05:14

Hierholzer's Algorithm
10:48

Quiz
3 questions

In this lecture we will define Hamiltonian Paths and Circuits. 

Hamiltonian Paths and Circuits
05:33

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

Hamiltonian Decomposition
01:33

Ore's Theorem
04:28

Dirac's Theorem
03:30

Quiz
3 questions

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

Shortest Path Problem
13:59

Five Room Puzzle
04:22

Knight's Tour
03:25
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Trees
10 Lectures 57:02

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

Trees
05:26

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

Tree Types
03:49

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. 

Rooted Trees
06:24

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

Tree Structures
05:36

Quiz
5 questions

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

Binary Trees
07:50

Spanning Trees
04:44

Quiz
4 questions

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

Binary Expression Trees
06:36

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

Tree Traversal
14:02

Quiz
3 questions

Forests
01:36
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Graph Match
6 Lectures 18:04

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

Graph Match
06:50


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

Berge's Lemma
02:30

Vertex and Edge Cover
03:53

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

König's Theorem
01:22

Quiz
5 questions
About the Instructor
Miran Fattah
4.3 Average rating
374 Reviews
5,387 Students
6 Courses
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.