About This Chapter
Who's It For?
Anyone who needs help learning or mastering graph theory material will benefit from the lessons in this chapter. There is no faster or easier way to learn graph theory. Among those who would benefit are:
- Students who have fallen behind in understanding working with graphs
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about graph theory
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Graph Theory chapter exam.
Why It Works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Graph Theory chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any graph theory question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in a graph theory unit of a standard contemporary math course. Topics covered include:
- Fleury's Algorithm
- Eulerizing graphs
- Euler's circuits, paths & theorems
- Hamilton circuits & paths
- Specific concepts & terminology explained
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.
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.
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.
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.
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.
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.
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.
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!
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.
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.
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.
12. How to Find the Slope of a Perpendicular Line
In this lesson, we'll introduce the concept of slope and then discuss the relationship between the slopes of two perpendicular lines. Knowing this simple relationship will save you time on many math problems!
13. Intersection in Math: Definition & Symbol
In this lesson, you will learn about how intersection works in math for both lines and sets. Also, learn how you can easily communicate intersection to others by using a unique symbol.
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Other chapters within the Contemporary Math: Help and Review course
- Mathematical Reasoning & Problem-Solving: Help and Review
- How to Solve Word Problems: Help and Review
- Statistics Overview: Help and Review
- Probability Overview: Help and Review
- Understanding Discrete Probability Distributions: Help and Review
- The Normal Curve & Continuous Probability Distributions: Help and Review
- The Mathematics of Voting: Help and Review
- The Mathematics of Apportionment: Help and Review
- Operations with Basic Algebraic Expressions
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Performing Basic Arithmetic
- Operations with Monomials and Polynomials
- Number Line & the Coordinate Graph