# Ch 48: ORELA Math: Graph Theory

### About This Chapter

## ORELA Math: Graph Theory - Chapter Summary

These short videos are an enticing and convenient way to review the graph theory concepts you'll likely encounter on the ORELA Math certification assessment. This chapter covers the ideas you need to know, such as:

- Basic graph theory and terminology
- Euler's theorems, paths and circuits
- The Fleury algorithm
- The sum of degrees
- Mathematical models
- Hamilton paths and circuits
- Complete and weighted graphs

The quick multiple-choice quiz after each lesson provides an important opportunity to test your understanding of graph theory and gain comfort with the material. If there are any areas you'd like to give additional review, use the video transcripts- they highlight key ideas, making them easy to locate.

### Objectives of the ORELA Math: Graph Theory Chapter

The material in this chapter focuses on the graph theory concepts you're supposed to know for ORELA certification. Use the lesson quizzes to see the ORELA format--we mimic the assessment style so you can get practice for your exam.

Four and a quarter hours are permitted for ORELA Math test-takers. The computer-administered assessment includes approximately 150 multiple-choice questions that assess competency in five content areas: measurement and geometry; statistics, probability and discrete math; trigonometry and calculus; math processes and number sense; and patterns, algebra and functions. The first four make up 19% of the exam each, and the final (patterns, algebra and functions) makes up the remaining 24%.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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!

### 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.

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### Other Chapters

Other chapters within the ORELA Mathematics: Practice & Study Guide course

- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Functions
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Properties of Triangles
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Conic Sections
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Functions
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Trigonometric Identities
- ORELA Math: Sequences & Series
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards