Physical world and mathematics

Granulite

Granulite is a high-grade metamorphic rock with an even granular texture and hydroxyl-free minerals, also naming the granulite facies formed at 700 to 1100 °C.

Granulometry is the determination of the particle-size distribution of a granular material or powder, by techniques such as sieving, laser diffraction, and sedimentation; the result is a distribution, not a single number.

GRAPES

GRAPES (Global/Regional Assimilation and PrEdiction System) is a numerical weather prediction system developed by the China Meteorological Administration, built from 2001 to 2005 and used for global and regional forecasting in China.

Graph (discrete mathematics)

A graph in discrete mathematics is a structure of vertices joined by edges that models relationships; its study, graph theory, dates to Euler's 1736 Königsberg analysis.

Graph Cartesian product

The graph Cartesian product, denoted G square H and also called the box product, is a binary operation on graphs whose vertices are ordered pairs, adjacent when they differ in exactly one coordinate.

Graph drawing

Graph drawing, also called graph layout, is the branch of computer science that positions graph vertices and routes edges to render networks as readable diagrams.

Graph embedding

A graph embedding is a placement of a graph on a surface with vertices as points and edges as noncrossing curves, the central object of topological graph theory.

Graph Fourier transform

The graph Fourier transform decomposes a signal defined on a graph's vertices into components carried by the eigenvectors of the graph Laplacian, like the classical Fourier transform.

Graph invariant

A graph invariant, also called a graph property, is a quantity of a graph that depends only on its structure, not on vertex labels or how it is drawn.

Graph isomorphism

Graph isomorphism, also called testing isomorphic graphs, asks whether two graphs have the same structure up to renaming vertices; László Babai's 2015 quasipolynomial algorithm was a major breakthrough.

Graph isomorphism problem

The graph isomorphism problem asks whether two graphs can be relabeled to be identical. It lies in NP, and László Babai gave a quasipolynomial-time algorithm in 2015.

Graph minor

A graph minor is a graph derived from another by deleting or contracting edges and removing isolated vertices; Robertson and Seymour developed the theory of it.

Graph of a function

The graph of a function, also called a function graph, is the set of all ordered pairs relating each input to its output, plotted as points in the plane.

Graph partitioning

Graph partitioning divides a graph's vertices into roughly equal blocks while minimizing the edges crossing between blocks, an NP-hard problem used in parallel computing and VLSI design.

Graph reduction

Graph reduction is an implementation technique for functional programming languages in which a program is a graph rewritten in place during evaluation, introduced by Christopher Wadsworth in 1971.

Graph removal lemma

The graph removal lemma is a theorem in extremal graph theory: a graph with few copies of a fixed graph H can be made H-free by deleting few edges.

Graph spectrum

The graph spectrum is the set of eigenvalues of a graph's adjacency matrix, real because the matrix is symmetric, and the subject of spectral graph theory.

Graph state

A graph state is a multi-qubit entangled quantum state defined by a simple graph, with each edge a CZ gate; its cluster states are the universal resource of the one-way quantum computer.

Graph structure theorem

The graph structure theorem, proved by Neil Robertson and Paul Seymour, describes every graph with no fixed graph H as a minor as built from pieces embeddable in a surface.

Graph theoretical analysis

Graph theoretical analysis models systems as graphs of nodes and edges and computes summary measures, an interdisciplinary toolset applied to brain networks, power grids, and social networks.

Graph theory

Graph theory is the branch of mathematics that studies graphs, structures of vertices and edges modeling pairwise relationships, originating in Euler's 1735 analysis of the Königsberg bridges problem.

Graph Theory with Applications

Graph Theory with Applications is a graduate-level graph theory textbook by J. A. Bondy and U. S. R. Murty, published in 1976 and praised by reviewers as outstanding.

GraphBLAS

GraphBLAS (Graph Basic Linear Algebra Subprograms) is a specification for an API that expresses graph algorithms as sparse matrix operations over semirings, developed by the open GraphBLAS Forum and modeled on the BLAS standard.

Graphdiyne

Graphdiyne is a two-dimensional carbon allotrope of sp² benzene rings joined by diacetylenic linkages, first synthesized in 2010, with applications in batteries, catalysis, and electronics.

Graphene

Graphene is a single layer of carbon atoms arranged in a hexagonal honeycomb lattice, first isolated in 2004 at the University of Manchester and prized for its strength and conductivity.

Graphene aerogel

Aerographene, also called graphene aerogel, is a porous three-dimensional solid of graphene sheets and air, over 99 percent empty, combining ultralow density with graphene's electrical and thermal conductivity.

Graphene biosensor

A graphene biosensor is a device that uses graphene, a one-atom-thick sheet of carbon atoms, as the transducer converting a biological target's binding into an electrical or optical signal.

Graphene capillaries

Graphene capillaries are nanometer-scale channels with atomically flat graphene walls, introduced at the University of Manchester in 2016 to study how water and ions move through tiny spaces.

Graphene composites

Graphene composites are materials that incorporate graphene, graphene oxide, or reduced graphene oxide into polymer, metal, ceramic, or cement matrices to improve strength and conductivity.