Graph operations | Graph families | Intersection classes of graphs
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this. Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the ΞΈ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph. Hassler Whitney proved that with one exceptional case the structure of a connected graph G can be recovered completely from its line graph. Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs are characterized by nine forbidden subgraphs and can be recognized in linear time. Various extensions of the concept of a line graph have been studied, including line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs. (Wikipedia).
Overview of points lines plans and their location
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Name the segments in the given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
What is a line segment and ray
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
CCSS How to Label a Line, Line Segment and Ray
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Naming the rays in a given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Name the opposite rays in the given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Unicursal Graphs and Unicursal Lines | Semi-Eulerian Trails, Graph Theory
What are unicursal graphs and unicursal lines in graph theory? We'll define them, and provide examples in today's lesson! A unicursal line of a graph is an open trail containing every edge of the graph. By definition of open trail, it contains each edge exactly once, but may repeat vertic
From playlist Graph Theory
Position-Time Graphs: Changing Speed Motion
Many Physics students become frustrated and confused once the topic of Kinematic Graphing is covered. But it doesn't need to be that way. And with The Physics Classroom's set of videos on the topic, you will rise to the top of the class. This Position-Time Graph video focuses on the meanin
From playlist Kinematics Video Tutorial Series
Position-Time Graphs: Constant Speed Motion
Many Physics students become frustrated and confused once the topic of Kinematic Graphing is covered. But it doesn't need to be that way. And with The Physics Classroom's set of videos on the topic, you will rise to the top of the class. This Position-Time Graph video focuses on the meanin
From playlist Kinematics Video Tutorial Series
Walking Position, Velocity and Acceleration as a Function of Time Graphs
This lesson builds on what we learned about position as a function of time graphs. We start with velocity as a function of time graphs, determine what the motion would look like and then draw position and acceleration as a function of time graphs. We use the concepts of slope and tangent
From playlist Motion in One Dimension - AP Physics 1
Velocity-Time Graphs: Changing Velocity Motion
Many Physics students become frustrated and confused once the topic of Kinematic Graphing is covered. But it doesn't need to be that way. Β This is the second of four videos explaining the details for understanding velocity-time graphs. This video focuses on changing velocity motions, disti
From playlist Kinematics Video Tutorial Series
R - Graphs - Line Graphs with Error Bars in Ggplot2
Recorded: Fall 2015 Lecturer: Dr. Erin M. Buchanan This video covers the basic ideas of functions using R - topics include: - ggplot2 - line graphs with one independent variable - line graphs with two independent variables - error bars - stat summary - changing the legends, axes labels, a
From playlist Learn R + Statistics
Identifying Characteristics of Graphs
I define and discuss the following vocabulary: Functions and the Vertical Line Test at 3:00 Relations at 8:01 Discrete Graphs at 11:35 Continuous Graphs at 13:20 Vertical and Horizontal Line of Symmetry at 14:38 Smooth Curves at 17:22 Increasing Function and Decreasing Function 21:45 Ident
From playlist Algebra 1
AP Calculus AB: Lesson 2.6 Tangent Line Approximations
AP Calculus AB Unit 2: Understanding the Derivative Lesson 6: Tangent Line Approximations
From playlist AP Calculus AB
Velocity-Time Graphs: Constant Speed Motion
Many Physics students become frustrated and confused once the topic of Kinematic Graphing is covered. But it doesn't need to be that way. Β This is the first of four videos explaining the details for understanding velocity-time graphs. This video focuses on constant velocity motions, distin
From playlist Kinematics Video Tutorial Series
Given a line segment name the two planes that intersect
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure