Mathematical chess problems | Parametric families of graphs
In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move. More specifically, an king's graph is a king's graph of an chessboard. It is the map graph formed from the squares of a chessboard by making a vertex for each square and an edge for each two squares that share an edge or a corner. It can also be constructed as the strong product of two path graphs. For an king's graph the total number of vertices is and the number of edges is . For a square king's graph this simplifies so that the total number of vertices is and the total number of edges is . The neighbourhood of a vertex in the king's graph corresponds to the Moore neighborhood for cellular automata.A generalization of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph in which each bounded face is a quadrilateral and each interior vertex has at least four neighbors) by adding the two diagonals of every quadrilateral face of the squaregraph. In the drawing of a king's graph obtained from an chessboard, there are crossings, but it is possible to obtain a drawing with fewer crossings by connecting the two nearest neighbors of each corner square by a curve outside the chessboard instead of by a diagonal line segment. In this way, crossings are always possible. For the king's graph of small chessboards, other drawings lead to even fewer crossings; in particular every king's graph is a planar graph. However, when both and are at least four, and they are not both equal to four, is the optimal number of crossings. (Wikipedia).
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
Graph Theory: 02. Definition of a Graph
In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio
From playlist Graph Theory part-1
Platonic graphs and the Petersen graph
In this tutorial I show you to construct the five platonic graphs and the Peterson graph in Mathematica and we use some of the information in the previous lectures to look at some of the properties of these graphs, simply by looking at their graphical representation.
From playlist Introducing graph theory
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph Theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
What are Cycle Graphs? | Graph Theory, Graph Cycles, Cyclic Graphs
What are cycle graphs? We have talked before about graph cycles, which refers to a way of moving through a graph, but a cycle graph is slightly different. A cycle graph is what you would get if you took the vertices and edges of a graph cycle. We can think of cycle graphs as being path gra
From playlist Graph Theory
Graph Theory: 03. Examples of Graphs
We provide some basic examples of graphs in Graph Theory. This video will help you to get familiar with the notation and what it represents. We also discuss the idea of adjacent vertices and edges. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https
From playlist Graph Theory part-1
Tree Graphs - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Behavioral Experiments in Strategic Networks - Michael Kearns
Michael Kearns University of Pennsylvania March 8, 2010 For four years now, we have been conducting "medium-scale" experiments in how human subjects behave in strategic and economic settings mediated by an underlying network structure. We have explored a wide range of networks inspired by
From playlist Mathematics
Extremal Combinatorics with Po-Shen Loh - 05/01 Fri
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Robert Bosch - Figurative Subgraphs - G4G13 Apr 2018
Given a graph (a collection of dots and line segments connecting certain pairs of dots) and a target image, we form subgraphs that look like the image.
From playlist G4G13 Videos
Data Science - Part X - Time Series Forecasting
For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of Time Series forecasting techniques and the process of creating effective for
From playlist Data Science
Inconsistent systems of equations | Algebra II | Khan Academy
Systems of equations without a solution Watch the next lesson: https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_tutorial_precalc/v/infinite-solutions-to-systems?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/
From playlist Mathematics I | High School Math | Khan Academy
Jane Hillston (DDMCS@Turing): Moment analysis, model reduction and London bike sharing
Complex models in all areas of science and engineering, and in the social sciences, must be reduced to a relatively small number of variables for practical computation and accurate prediction. In general, it is difficult to identify and parameterize the crucial features that must be incorp
From playlist Data driven modelling of complex systems
Bruno Courcelle: Recognizable sets of graphs: algebraic and logical aspects
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Aspects of Computer Science
From playlist Contributed talks One World Symposium 2020
MIT 15.S50 Poker Theory and Analysis, IAP 2015 View the complete course: http://ocw.mit.edu/15-S50IAP15 Instructor: Kevin Desmond This lecture focuses on how to play the pre-flop as close to optimally as possible by analyzing several scenarios. License: Creative Commons BY-NC-SA More inf
From playlist MIT 15.S50 Poker Theory and Analysis, IAP 2015
This is Lecture 17 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture15.pdf More inf
From playlist CSE373 - Analysis of Algorithms 2016 SBU
Creating a Time-Series Graph with Excel
This demonstration shows you how to create a time-series graph in Excel. This demonstration corresponds to the Introduction to Statistics, Think & Do textbook by Scott Stevens (http://www.StevensStats.com).
From playlist Excel Demonstrations