Regular graphs | Individual graphs
In the mathematical field of graph theory, the Dejter graph is a 6-regular graph with 112 vertices and 336 edges. The Dejter graph isobtained by deleting a copyof the Hamming code of length 7 from the binary7-cube. The Dejter graph, and by extension any graph obtained by deleting a Hamming code of length 2r-1 from a(2r-1)-cube, is a symmetric graph.In particular, the Dejter graph admits a 3-factorization into twocopies of the Ljubljana graph, which is the third smallest existing semi-symmetric cubic graph of regular degree 3. The Ljubljana graph has girth 10. In fact, it is proven that the Dejter graph can be 2-colored, say in the color set {red, blue}, as in the top figure to the right, so that both the resulting edge-monochromatic red and blue vertex-spanning subgraphs are copies of the Ljubljana graph. These two copies contain exactly the 112 vertices of the Dejter graph and 168 edges each, having both copies girth 10, while the Dejter graph has girth 6 and the 7-cube girth 4. It seems that the Dejter graph is the smallest symmetric graph having a connected self-complementary vertex-spanning semi-symmetric cubic subgraph. Both the red and blue vertex-spanning Ljubljana subgraphs of the Dejter graph can be presented as covering graphs of the Heawood graph, namely as 8-covers of the Heawood graph. This is suggested in each of the two representations of the Ljubljana graph, (red above, blue below, both to the right), by alternately coloring the inverse images of successive vertices of the Heawood graph, say in black and white (better viewed by twice clicking on images for figure enlargements), according to the Heawood graph bipartition. Each such inverse image is formed by the 8 neighbors, along a fixed coordinate direction of the 7-cube, of the half of the Hamming code having a fixed weight, 0 or 1. By exchanging these weights via the permutation (0 1), one can pass from the adjacency offered by the red Ljubljana graph to the one offered by the blue Ljubljana graph, or vice versa. One seventh of the Dejter graph appears in a separate figure down below that can be obtained from the two resulting copies of the Heawood graph. (Wikipedia).
Learn how to graph the parent graph of a quadratic equation in standard form using a table
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
What are the transformations of vertex form of a quadratic compared to standard form
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
How to determine the domain and range of a quadratic using its vertex
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Lecture quadratic functions and it's solutions
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
What do I need to know to graph a quadratic in vertex form
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Summary for graphing a quadratic in vertex form
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Finding the axis of symmetry for a parabola and graph
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Learning how to graph and determine characteristics of a quadratic using vertex formula
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetry, to p
From playlist Graph a Quadratic in Standard Form | ax^2+bx+c
What do I have to know to graph a quadratic in standard form
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
Irina Gelbukh 2023: The Reeb graph of a smooth function encodes the function class and manifold type
Title: How the Reeb graph of a smooth function encodes the class of the function and the type of the manifold Abstract: The Reeb graph of a function is a space obtained by contracting connected components of the function's level sets to points. Computer scientists mostly deal with Morse f
From playlist Vietoris-Rips Seminar
Graphs In Data Structures | Graph Representation In Data Structure | Data Structures | Simplilearn
This data structures tutorial is dedicated to helping beginners understand the graphs in data structures. In this tutorial, you will understand the fundamentals and terminologies of the graph data structure, their types and their representation using different methods. The graphs in this t
From playlist Data Structures & Algorithms [2022 Updated]
What are Planar Graphs? | Graph Theory
What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t
From playlist Graph Theory
Lecture 19 - Degree Sequences & Invariants
This is Lecture 19 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2019.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Empty Graph, Trivial Graph, and the Null Graph | Graph Theory
Whenever we talk about something that is defined by sets, it is important to consider the empty set and how it fits into the definition. In graph theory, empty sets in the definition of a particular graph can bring on three types/categories of graphs. The empty graphs, the trivial graph, a
From playlist Graph Theory
What is the limit of a sequence of graphs?? | Benjamini-Schramm Convergence
This is an introduction to the mathematical concept of Benjamini-Schramm convergence, which is a type of graph limit theory which works well for sparse graphs. We hope that most of it is understandable by a wide audience with some mathematical background (including some prior exposure to g
From playlist Summer of Math Exposition Youtube Videos
Vertex Cuts in Graphs (and a bit on Connectivity) | Graph Theory, Vertex-Connectivity
What is a vertex cut of a graph? And how can we use vertex cuts to describe how connected a graph is? We have discussed cut vertices and connected graphs before, but by tying them together in a way, we are able to characterize different levels of connectivity in graphs. The focus of this l
From playlist Graph Theory
Vertex Connectivity of a Graph | Connectivity, K-connected Graphs, Graph Theory
What is vertex connectivity in graph theory? We'll be going over the definition of connectivity and some examples and related concepts in today's video graph theory lesson! The vertex connectivity of a graph is the minimum number of vertices you can delete to disconnect the graph or make
From playlist Graph Theory
Lecture 10 - Data Structures for Graphs
This is Lecture 10 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2007. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/2007/lecture10.pdf More informa
From playlist CSE373 - Analysis of Algorithms - 2007 SBU
Lecture 20 - Trees and Connectivity
This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
How to analyze a quadratic function to graph
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials