Graph invariants | Geometric graph theory

Dimension (graph theory)

In mathematics, and particularly in graph theory, the dimension of a graph is the least integer n such that there exists a "classical representation" of the graph in the Euclidean space of dimension n with all the edges having unit length. In a classical representation, the vertices must be distinct points, but the edges may cross one another. The dimension of a graph G is written: . For example, the Petersen graph can be drawn with unit edges in , but not in : its dimension is therefore 2 (see the figure to the right). This concept was introduced in 1965 by Paul Erdős, Frank Harary and William Tutte. It generalises the concept of unit distance graph to more than 2 dimensions. (Wikipedia).

Dimension (graph theory)
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Diameter of a Graph | Graph Theory

What is the diameter of a graph in graph theory? This is a simple term we will define with examples in today's video graph theory lesson! Remember that the distance between two connected vertices in a graph is the length of a shortest path between those vertices. Here's my lesson on dist

From playlist Graph Theory

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Graph Theory: 51. Eccentricity, Radius & Diameter

Eccentricity, radius and diameter are terms that are used often in graph theory. They are related to the concept of the distance between vertices. The distance between a pair of vertices is the length of a shortest path between them. We begin by reviewing some of the properties of dista

From playlist Graph Theory part-9

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Diameter and Radius of Graphs | Graph Theory

We define the radius of a graph and the diameter of a graph using the eccentricity of vertices. We relate these terms intuitively back to circles and discuss several examples of graph diameter and graph radius. We also introduce a theorem stating the diameter of a graph is bounded between

From playlist Graph Theory

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Graph Theory: Basic Definitions

This video describes some basic definitions associated with graph theory.

From playlist Basics: 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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Graph Theory: 02. Definition of a Graph

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From playlist Graph Theory part-1

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Wolfram Physics Project: Working Session Mar. 30, 2021 [Dimension Evolution in the Early Universe]

This is a Wolfram Physics Project working session on dimension evolution in the early Universe in the Wolfram Model. Begins at 7:35 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the

From playlist Wolfram Physics Project Livestream Archive

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Graph Theory Talk: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues

Graph Theory Stuff: Graphs, Edges, Vertices, Adjacency Matrix and it's Eigenvalues

From playlist Graph Theory

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Vladimir KAZAKOV - Conformal Fishnet Theory in Any Dimension

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From playlist Integrability, Anomalies and Quantum Field Theory

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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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Graph Theory: 50. Maximum vs Maximal

Here we describe the difference between two similar sounding words in mathematics: maximum and maximal. We use concepts in graph theory to highlight the difference. In particular, we define an independent set in a graph and a component in a graph and look at some examples. -- Bits of Gra

From playlist Graph Theory part-9

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What Every Physicist Should Know About String Theory: Edward Witten

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From playlist Strings 2015 conference

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Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018

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From playlist Plenary Lectures

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Joel Friedman - Sheaves on Graphs, L^2 Betti Numbers, and Applications.

Joel Friedman (University of British Columbia, Canada) Sheaf theory and (co)homology, in the generality developed by Grothendieck et al., seems to hold great promise for applications in discrete mathematics. We shall describe sheaves on graphs and their applications to (1) solving the

From playlist T1-2014 : Random walks and asymptopic geometry of groups.

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High dimensional expanders – Alexander Lubotzky – ICM2018

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From playlist Plenary Lectures

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Omer Bobrowski: Random Simplicial Complexes, Lecture I

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From playlist Workshop: High dimensional spatial random systems

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Order and Size of a Graph | Graph Theory

What is the order and size of a graph? We'll go over them both in this math lesson! A graph is an ordered pair with a vertex set and an edge set. The order of a graph is the cardinality of its vertex set, which is the number of vertices in the graph. The size of a graph is the cardinality

From playlist Graph Theory

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Oliver SCHNETZ - 2010-2020: a Decade of Quantum Computing

Supported by Dirk Kreimer, in 2010 I started analyzing and calculating high loop-order amplitudes in perturbative quantum field theory. The main tools were graphical functions, generalized single-valued hyperlogarithms (GSVHs), and the c_2-invariant. I will report on the progress that has

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

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Graph theory | Existential theory of the reals | Petersen graph | Complete bipartite graph | Chromatic number | Mathematics | Complete graph | Star (graph theory) | Frank Harary | Paul Erdős | Unit distance graph | Degree (graph theory) | Wheel graph | Euclidean space | Simplex | Immersion (mathematics)