Graph theory

Dominator (graph theory)

In computer science, a node d of a control-flow graph dominates a node n if every path from the entry node to n must go through d. Notationally, this is written as d dom n (or sometimes d ≫ n). By definition, every node dominates itself. There are a number of related concepts: * A node d strictly dominates a node n if d dominates n and d does not equal n. * The immediate dominator or idom of a node n is the unique node that strictly dominates n but does not strictly dominate any other node that strictly dominates n. Every node, except the entry node, has an immediate dominator. * The dominance frontier of a node d is the set of all nodes ni such that d dominates an immediate predecessor of ni, but d does not strictly dominate ni. It is the set of nodes where d's dominance stops. * A dominator tree is a tree where each node's children are those nodes it immediately dominates. The start node is the root of the tree. (Wikipedia).

Dominator (graph theory)
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Subgraphs

A subgraph consist of nodes and edges of a larger graph. In this tutorial I show you what a subgraph is and present an elegant representation in Mathematica. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale an

From playlist Introducing graph theory

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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

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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

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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

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Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o

From playlist Graph Theory FAQs

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Planar graphs

Planar graphs, What are planar graphs? In this video we take a look at what a planar graph is and how Mathematica can check to see if a graph is planar. In short, a planar graph is one that can be drawn in the plane such that no edges cross. If you want to learn more about Mathematica,

From playlist Introducing graph theory

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The Definition of a Graph (Graph Theory)

The Definition of a Graph (Graph Theory) mathispower4u.com

From playlist Graph Theory (Discrete Math)

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Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

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Dominating Sets and Domination Number of Graphs | Graph Theory

A vertex is said to dominate itself and its neighbors. Then, a dominating set of a graph G is a vertex subset S of G such that every vertex in G is dominated by some vertex in S. This means every vertex in G-S is adjacent to some vertex in S. A dominating set of minimum cardinality is a mi

From playlist Graph Theory

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Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman

Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit

From playlist Mathematics

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Measure Theory - Part 10 - Lebesgue's dominated convergence theorem [dark version]

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From playlist Measure Theory [dark version]

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Math Exposition Video 1:Introduction to the Probabilistic Method

This video is (hopefully) going to be part of a series of me tyring to explain mathematics close to my heart :-) This is also going to be my maiden entry into 3Blue1Brown's Summer of Math Exposition. I talk about a couple of intriguing examples,one on Ramsey numbers and the other on domina

From playlist Summer of Math Exposition Youtube Videos

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Joel Kamnitzer - Symplectic Resolutions, Coulomb Branches, and 3d Mirror Symmetry 5/5

In the 21st century, there has been a great interest in the study of symplectic resolutions, such as cotangent bundles of flag varieties, hypertoric varieties, quiver varieties, and affine Grassmannian slices. Mathematicians, especially Braden-Licata-Proudfoot-Webster, and physicists obser

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Introduction to Graph Theory: A Computer Science Perspective

In this video, I introduce the field of graph theory. We first answer the important question of why someone should even care about studying graph theory through an application perspective. Afterwards, we introduce definitions and essential terminology in graph theory, followed by a discuss

From playlist Graph Theory

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Measure Theory - Part 10 - Lebesgue's dominated convergence theorem

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From playlist Measure Theory

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Why the West Rules -- For Now

October 21, 2010 - Ian Morris discusses why the western world dominates the planet today and how it came to gain control. He suggests that looking at long-term history can tell us why this happened -- and what might happen next. This talk was presented as part of the Classes Without Quizz

From playlist Reunion Homecoming

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The SYK Model by David Gross

Kavli Distinguished Lecture SPEAKER: David Gross (KITP - University of California, Santa Barbara) DATE & TIME: 08 January 2018, 09:00 to 10:30 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Abstract: A perspective on large N theories: their role in quantum field theory, in gauge-gravit

From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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André M. de Roos: On the relevance and irrelevance of dynamic energy budget models for ...

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 Dynamical Systems and Ordinary Differential Equations

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Lorenzo Ruffoni - Graphical splittings of Artin kernels

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Lorenzo Ruffoni, Florida State University Title: Graphical splittings of Artin kernels Abstract: A main feature of the theory of right-angled Artin groups (RAAGs) consists in the fact that the algebraic properties of the g

From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

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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

Related pages

Control-flow graph | Quadratic growth | Tree (graph theory)