Ch 47: GACE Math: Graph Theory

About This Chapter

Learn about all of the detailed components of graph theory using these video lessons. Each lesson comes with a short quiz for you to assess your comprehension of the material as you prepare for similar questions on the GACE Math assessment.

GACE Math: Graph Theory - Chapter Summary

These chapter lessons will teach you all you need to know regarding graph theory in mathematics as part of your preparation for the GACE Math assessment. The topics below are covered in detail throughout this chapter:

  • Key graph theory terminology
  • Hamilton circuits and paths
  • Weighted and complete graphs
  • Euler's theorems, paths and circuits
  • Fleury's algorithm

Review these videos from a smartphone or tablet when you're not near a computer. You can take a chapter exam after you're done with all of the quizzes to further demonstrate your familiarity with graph theory.

7 Lessons in Chapter 47: GACE Math: Graph Theory
Test your knowledge with a 30-question chapter practice test
Graph Theory Concepts and Terminology

1. 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

2. 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

3. 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

4. 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

5. 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.

Hamilton Circuits and Hamilton Paths

6. 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

7. 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.

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

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Other Chapters

Other chapters within the GACE Mathematics (522): Practice & Study Guide course

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