Ch 9: Graph Theory Lesson Plans

About This Chapter

The Graph Theory chapter of this course is designed to help you plan and teach graphs theory concepts in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Graph Theory chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday Graph theory intro and basic concepts Graph theory, types of vertices, degree of a vertex, edges, path and disconnected and connected graphs
Tuesday Euler paths, circuits and theorems Euler path, semi-Eulerian, Euler circuit, Eulerian and Euler's circuit and path theorems
Wednesday Fleury's algorithm and Eulerizing graphs Fleury's algorithm and Eulerizing and semi-Eulerizing graphs
Thursday Hamilton circuits and paths Hamilton path, Hamilton circuit, weighted and complete graphs
Friday The traveling salesman problem Solving the traveling salesman problem, nearest and repeated nearest neighbor approaches, brute force method and the cheapest link method

11 Lessons in Chapter 9: Graph Theory Lesson Plans
Test your knowledge with a 30-question chapter practice test
Introduction to Graph Theory

1. Introduction to Graph Theory

After watching this video lesson, you will understand what graph theory is. You will also see what a graph looks like and be introduced to the basic vocabulary used in graph theory.

Graph Theory Concepts and Terminology

2. Graph Theory Concepts and Terminology

After watching this video lesson, you will better understand the workings of a graph in graph theory. Learn the key terms that you will see and what they look like on the graph. Also, learn how to navigate a graph.

Euler Paths and Euler's Circuits

3. Euler Paths and Euler's Circuits

Watch this video lesson, and you will see how you can turn a math problem into a challenging brain game. Learn what it means for a graph to be Eulerian or semi-Eulerian.

Mathematical Models of Euler's Circuits & Euler's Paths

4. Mathematical Models of Euler's Circuits & Euler's Paths

Watch this video lesson to see how Euler paths and circuits are used in the real world. Learn how to solve real-world problems by drawing a graph and finding Euler paths and circuits.

Euler's Theorems: Circuit, Path & Sum of Degrees

5. Euler's Theorems: Circuit, Path & Sum of Degrees

Watch this video lesson, and you will understand how Euler's circuit theorem, Euler's path theorem, and Euler's sum of degrees theorem will help you analyze graphs. Also, get some practice with the quiz.

Fleury's Algorithm for Finding an Euler Circuit

6. Fleury's Algorithm for Finding an Euler Circuit

In this video lesson, you will learn a method for finding an Euler circuit. Learn the one criterion that is the basis for all your decisions when choosing a route.

Eulerizing Graphs in Math

7. Eulerizing Graphs in Math

After watching this video lesson, you will be able to Eulerize any graph. Learn what it takes to create a Eulerian graph from a non-Eulerian graph. Learn what Fleury's algorithm has to do with all of this.

Hamilton Circuits and Hamilton Paths

8. Hamilton Circuits and Hamilton Paths

After watching this video lesson, you will be able to determine how many Hamilton circuits a particular graph has, as well as find Hamilton circuits and paths in these graphs. Then, check out our quiz questions to test your new knowledge!

Assessing Weighted & Complete Graphs for Hamilton Circuits

9. Assessing Weighted & Complete Graphs for Hamilton Circuits

Watch this video lesson and you will discover how to find a Hamilton circuit in a weighted graph. You'll also learn how to find the number of Hamilton circuits in a complete graph.

The Traveling Salesman Problem in Computation

10. The Traveling Salesman Problem in Computation

Watch this video lesson to learn about the traveling salesman problem. Learn how to identify these types of problems. This is a problem that even computers have a hard time figuring out. Learn why this is so.

Methods of Finding the Most Efficient Circuit

11. Methods of Finding the Most Efficient Circuit

After watching this video lesson, you will understand several ways in which you can solve the famous traveling salesman problem. You'll also learn the drawbacks to each solution method.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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