Graph families | Planar graphs

Lattice graph

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space , forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8 × 8 square grid". The term lattice graph has also been given in the literature to various other kinds of graphs with some regular structure, such as the Cartesian product of a number of complete graphs. (Wikipedia).

Lattice graph
Video thumbnail

Graph Neural Networks, Session 1: Introduction to Graphs

Examples of Graph representation of data Motivation for doing machine learning on Graphs

From playlist Graph Neural Networks (Hands-on)

Video thumbnail

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

Video thumbnail

What is a Path Graph? | Graph Theory

What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can

From playlist Graph Theory

Video thumbnail

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

Video thumbnail

The Definition of a Graph (Graph Theory)

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

From playlist Graph Theory (Discrete Math)

Video thumbnail

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

Video thumbnail

Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

Video thumbnail

Forbidden Patterns in Tropical Planar Curves by Ayush Kumar Tewari

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME 27 June 2022 to 08 July 2022 VENUE Madhava Lecture Hall and Online Algebraic geometry is the stu

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

Video thumbnail

Geoffrey Grimmett (University of Cambridge, UK) by Geoffrey Grimmett

PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This

From playlist First-Passage Percolation and Related Models 2022 Edited

Video thumbnail

Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids by Simon Trebst

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Video thumbnail

Konstantin Mischaikow (1/27/21): Nonlinear Dynamics in an Age of Heuristic Science

Title: Nonlinear Dynamics in an Age of Heuristic Science Abstract: Motivated by problems in systems and synthetic biology (but I believe the problems are common to multiscale systems and data driven science) I will argue the need for a new framework in which to discuss nonlinear dynamics

From playlist AATRN 2021

Video thumbnail

The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language

Graph-based percolation theory may be done in the Wolfram Language, here to aid in the understanding of viruses, their disassembly and eventual collapse. Capsids are protein nanocontainers that store and protect a virus’s genetic material in transit between hosts. Capsids consist of hundre

From playlist Wolfram Technology Conference 2020

Video thumbnail

Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings - Anne Thomas

Anne Thomas University of Sydney, NSW April 6, 2011 SPECIAL LECTURE Let Gamma be a non-cocompact lattice on a right-angled building X. Examples of such X include products of trees, or Bourdon's building I_{p,q}, which has apartments hyperbolic planes tesselated by right-angled p-gons and

From playlist Mathematics

Video thumbnail

Monomer Percolation by Kedar Damle

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Video thumbnail

Yimo Han - Assisting 4D-STEM data processing by machine learning and Bayesian optimization

Recorded 28 October 2022. Yimo Han of Rice University presents "Assisting 4D-STEM data processing by machine learning and Bayesian optimization" at IPAM's Mathematical Advances for Multi-Dimensional Microscopy Workshop. Abstract: From the highest-resolution electron ptychography to microme

From playlist 2022 Mathematical Advances for Multi-Dimensional Microscopy

Video thumbnail

Karen Vogtmann - Outer space for right-angled Artin groups

Karen Vogtman (Cornell University, USA) Right-angled Artin groups interpolate between free groups and free abelian groups, so one may think of their outer automorphism groups as interpolating between Out(F_n) and GL(n,Z). I will describe an Outer space for these automorphism groups which

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

Video thumbnail

Data structures: Introduction to graphs

See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described Graph data structure as a mathematical model. We have briefly described the concept of Graph and some of its applications. For practice

From playlist Data structures

Video thumbnail

Tathagata Basak: A monstrous(?) complex hyperbolic orbifold

I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster

From playlist Topology

Related pages

Graph (discrete mathematics) | Lattice (group) | Planar graph | Rook's graph | Lattice (order) | Group (mathematics) | Median graph | Regular graph | Unit distance graph | Integer triangle | Path graph | Cartesian product of graphs | Graph theory | Graph minor | Cycle graph | Bipartite graph | Integer | Complete graph | Lattice path | Embedding | Euclidean space | Pick's theorem | Bijection | Hanan grid