Lessons at the Edge - Parts-One-Two-&-Three-Complete

Two types of graphs are complete graphs and connected graphs. Complete graphs are graphs that have an edge between every single vertex in the graph. A connected graph is a graph in which it is possible to get from every vertex in the graph to every other vertex in the graph through a series of edges, called a path. By definition, every complete graph is a connected graph, but not every connected graph is a complete graph. Because of this, these two types of graphs have similarities and differences that make them each unique.

Being familiar with each of these types of graphs, and their similarities and differences allow us to better analyze and utilize each of them, so it is a good idea to tuck this new-found knowledge into your back pocket for future use!

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Laura Pennington Laura has taught collegiate mathematics and holds a master's degree in pure mathematics. Add to Add to Add to. Want to watch this again later? In this lesson, we will define connected graphs and complete graphs. Then we will go on to analyze the similarities and differences between these two types of graphs and use them to do an example involving graphs. Complete Graphs and Connected Graphs Suppose a contractor, Shelly, is creating a neighborhood of six houses that are arranged in such a way that they enclose a forested area. Similarities and Differences We will start with some similarities.

It is possible to get from every vertex in each of these types of graphs to every other vertex in the graph through a series of edges. All vertices in both graphs have a degree of at least 1. Both types of graphs are made up of exactly one part. Now, let's look at some differences between these two types of graphs. All complete graphs are connected graphs, but not all connected graphs are complete graphs. It only takes one edge to get from any vertex to any other vertex in a complete graph.

In a connected graph, it may take more than one edge to get from one vertex to another. In a connected graph with n vertices, a vertex may have any degree greater than or equal to 1. Examples Consider the graph shown in the image. Try it risk-free No obligation, cancel anytime. Want to learn more? Select a subject to preview related courses: Adding Edge CD We see that we only need to add one edge to turn this graph into a connected graph, because we can now reach any vertex in the graph from any other vertex in the graph. Lesson Summary In the branch of mathematics called graph theory, a graph is a collection of points called vertices , and line segments between those vertices that are called edges.

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Similarities and Differences

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Browse Articles By Category Browse an area of study or degree level. You are viewing lesson Lesson 11 in chapter 13 of the course:. Help and Review 22 chapters lessons 13 flashcard sets. Latest Lessons What is Military Time? Popular Lessons Symbolic Interaction Theory: Create an account to start this course today. Like this lesson Share. Not sure what college you want to attend yet? The videos on Study.

Students in online learning conditions performed better than those receiving face-to-face instruction. Explore over 4, video courses. Find a degree that fits your goals. What is a Triangular Prism? In this lesson, learn how to find the size inside volume and outside surface area of a triangular prism. Try it risk-free for 30 days. An error occurred trying to load this video.

Try refreshing the page, or contact customer support. Register to view this lesson Are you a student or a teacher? I am a student I am a teacher. What teachers are saying about Study. What is a Variable Expression? Are you still watching? Your next lesson will play in 10 seconds. Add to Add to Add to. Want to watch this again later? What is a Triangle Pyramid? What is a Rectangular Prism? What is a Rectangular Pyramid?

Surface Area of a Triangular Prism. Cones Lesson for Kids: What is a Cuboid Shape? What is a Polyhedron? Overview of Three-dimensional Shapes in Geometry. What is a Hemisphere in Math? What is a Prism? Common Core Math - Functions: Praxis Mathematics - Content Knowledge TExES Mathematics High School Algebra II: Triangular prisms are three-dimensional solids formed by putting rectangles and triangles together.

Definition of Triangular Prism Picture a box sitting on the floor. A triangular prism The Different Parts of a Triangular Prism If you cut your triangular prism apart and lay it flat on the table, you have created the net for your triangular prism, as shown in the image below. A net for a triangular prism Notice how your three dimensional triangular prism is made up two dimensional shapes, like rectangles and triangles.

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The parts of a triangular prism When two of the faces meet, they form a line segment called an edge. Triangular prism with vertices labelled When referring to parts of a prism, use the letters that have been assigned to each vertex. Finding Surface Area Surface area is the amount of space on the outside of an object. You can do this by using the formulas for area of rectangles and triangles or you could use this shortcut: Find the perimeter of the triangle base, the p.

Try it risk-free No obligation, cancel anytime. Want to learn more? Select a subject to preview related courses: Find the area of the triangle base, the A. Determine the height of the prism. Finding surface area Step One: To find the volume of a triangular prism, find the area of the triangular base and multiply by the height of the solid, like this: Find the area of the triangular base, the A. Find the height of the prism, the h. Unlock Your Education See for yourself why 30 million people use Study.

Become a Member Already a member? Earning College Credit Did you know… We have over college courses that prepare you to earn credit by exam that is accepted by over 1, colleges and universities. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Browse Articles By Category Browse an area of study or degree level. You are viewing lesson Lesson 9 in chapter 22 of the course:. Tutoring Solution 30 chapters lessons.

Real Numbers - Types and Working with Linear Equations in Working with Inequalities in Absolute Value Equations in Working with Complex Numbers in Systems of Linear Equations in Introduction to Quadratics in Working with Quadratic Functions in Graph Symmetry in Trigonometry Graphing with Functions in Basic Polynomial Functions in Working with Trigonometric Graphs