Graph families | Regular graphs
In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. An (r, g)-cage is an (r, g)-graph with the smallest possible number of vertices, among all (r, g)-graphs. A (3, g)-cage is often called a g-cage. It is known that an (r, g)-graph exists for any combination of r ≥ 2 and g ≥ 3. It follows that all (r, g)-cages exist. If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least vertices, and any cage with even girth g must have at least vertices. Any (r, g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage. There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3, 10)-cages, each with 70 vertices: the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3, 11)-cage: the Balaban 11-cage (with 112 vertices). (Wikipedia).
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)
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
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 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
What is a Clique? | Graph Theory, Cliques
What is a clique? A clique in graph theory is an interesting concept with a lot of depth to explore. We define the term and give some examples in today's math video lesson! A clique C of a graph G is usually defined as a subset of the vertex set of G such that every pair of distinct verti
From playlist Graph Theory
Bridging between mean-field and real glasses (Lecture 3) by Patrick Charbonneau
Program Entropy, Information and Order in Soft Matter ORGANIZERS: Bulbul Chakraborty, Pinaki Chaudhuri, Chandan Dasgupta, Marjolein Dijkstra, Smarajit Karmakar, Vijaykumar Krishnamurthy, Jorge Kurchan, Madan Rao, Srikanth Sastry and Francesco Sciortino DATE: 27 August 2018 to 02 November
From playlist Entropy, Information and Order in Soft Matter
Recent Results on Finite Group Lattice Gauge Theories - Sky Yang Cao
Members' Colloquium Topic: Recent Results on Finite Group Lattice Gauge Theories Speaker: Sky Yang Cao Affiliation: Member, School of Mathematics Date: March 20, 2023 The rigorous study of spin systems such as the Ising model is currently one of the most active research areas in probabil
From playlist Mathematics
Growing length scale in the short-time dynamics of glass-forming liquids by 5 Chandan Dasgupta
Indian Statistical Physics Community Meeting 2016 URL: https://www.icts.res.in/discussion_meeting/details/31/ DATES Friday 12 Feb, 2016 - Sunday 14 Feb, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community wh
From playlist Indian Statistical Physics Community Meeting 2016
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
Diophantine Analysis of affine cubic Markoff type Surfaces - Peter Sarnak
Speaker: Peter Sarnak (Princeton/IAS) Title: Diophantine Analysis of affine cubic Markoff type Surfaces More videos on http://video.ias.edu
From playlist Mathematics
PiTP 2015 - "A Theory of Symmetry Protected Topological (3 of 3)" - Xiao-Gang Wen
https://pitp2015.ias.edu/
From playlist 2015 Prospects in Theoretical Physics Program
Role of confinement on polymer conformations by Vani Vemparala
DISCUSSION MEETING INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Sanjib Sabhapandit, Samriddhi Sankar Ray and Prerna Sharma DATE: 14 February 2019 to 16 February 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalo
From playlist Indian Statistical Physics Community Meeting 2019
Varieties of Markoff Type: Arithmetic, Combinatorics, Dynamics - Alexander Gamburd
Members' Colloquium Topic: Varieties of Markoff Type: Arithmetic, Combinatorics, Dynamics Speaker: Alexander Gamburd Affiliation: City University of New York; Member, School of Mathematics Date: December 12, 2022 The Markoff equation x2+y2+z2=3xyz, which arose in his spectacular thesis (
From playlist Mathematics
Colloqui della Classe di Scienze: Reidun Twarock - Mathematical Virology - 03 novembre 2021
Mathematical Virology: A Novel Perspective on Virus Structure, Assembly and Disassembly with Applications in Virus Nanotechnology. Reidun Twarock (University of York, UK) Viral protein containers, called capsids, are repurposed for applications in virus nanotechnology, including gene the
From playlist Colloqui della Classe di Scienze
"How Glasses Relax and Go With the Flow" by Andrea Liu
All solids flow at high enough applied stress and melt at high enough temperature. Crystalline solids flow and premelt via localized particle rearrangements that occur preferentially at structural defects known as dislocations. The population of dislocations therefore controls both how cry
From playlist On Broken Glass (Spring 2021)
Graph theory full course for Beginners
In mathematics, graph #theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A #graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction i
From playlist Graph Theory
A formal definition of a Graph and its properties
From playlist Graph Theory
Mathematical theories start with axioms, but penultimate to that is the definition. When we go to learn, what's the best definition to commit to memory? Here we talk about Graph Theory and I give you 3 definitions to choose from. Which would you use?
From playlist Summer of Math Exposition 2 videos
Panorama of Mathematics: Stanislav Smirnov
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Stanislav Smirnov: "Cluster
From playlist Panorama of Mathematics