The graphs of Bessel functions look roughly like oscillating sine or cosine functions that decay proportionally to 1 /√ x ( see also their asymptotic forms below ), although their roots are not generally periodic, except asymptotically for large x.

These are graphs of ψ ( x, y, z ) functions which depend on the coordinates of one electron.

To see the elongated shape of ψ ( x, y, z )< sup > 2 </ sup > functions that show probability density more directly, see the graphs of d-orbitals below.

The graphs studied in graph theory should not be confused with the graphs of functions or other kinds of graphs.

The primary on-board high-level programming languages of most graphing calculators ( most often Basic variants, sometimes Lisp derivatives, and more uncommonly, C derivatives ) in many cases can glue together calculator functions — such as graphs, lists, matrices, etc.

It states that if f is continuously differentiable, then around most points, the zero set of f looks like graphs of functions pasted together.

The points where this is not true are determined by a condition on the derivative of f. The circle, for instance, can be pasted together from the graphs of the two functions.

The implicit function theorem is closely related to the inverse function theorem, which states when a function looks like graphs of invertible functions pasted together.

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

* plotting graphs and parametric plots of functions in two and three dimensions, and animating them

Its departures from traditional Make are most noticeable in pattern-matching in dependency graphs and build targets, as well as a number of functions which may be invoked allowing functionality like listing the files in the current directory.

In his theory of graphs, or geometrical representations of algebraic functions, there are valuable suggestions which have been worked out by others.

The libpf library includes functions for the generation and manipulation of hierarchical scene graphs, scene processing ( simulation, intersection, culling, and drawing tasks ), level-of-detail management, asynchronous database paging, dynamic coordinate systems, environment models, light points, and so on.

They also found that some of his graphs, which purportedly had been plotted from experimental data, had instead been produced using mathematical functions.

* Layered graph drawing methods ( often called Sugiyama-style drawing ) are best suited for directed acyclic graphs or graphs that are nearly acyclic, such as the graphs of dependencies between modules or functions in a software system.

On an open dense set they do behave like functions, but the Zariski closures of their graphs are more complex correspondences on the product showing ' blowing up ' and ' blowing down '.

By the late Shang oracle bone script, the graphs had already evolved into a variety of mostly non-pictographic functions, including all the major types of Chinese characters now in use.

Two countable vertex-transitive graphs are called quasi-isometric if the ratio of their distance functions is bounded from below and from above.

# Partial order reduction can be used ( on explicitly represented graphs ) to reduce the number of independent interleavings of concurrent processes that need to be considered.

# redirect Glossary_of_graph_theory # Weighted graphs and networks

* MST Parser ( C #) A non-projective dependency parser that searches for maximum spanning trees over directed graphs ( C # conversion of the Java code )

The BEST theorem shows that the number of Eulerian circuits in directed graphs can be computed in polynomial time, a problem which is # P-complete for undirected graphs.

# S. Lo, On Edge-Graceful labelings of graphs, Congressus Numerantium 50 ( 1985 ) pp. 231 – 241

# REDIRECT List of graphs # Grid

since the graphs of these are just rigid rotations of the roses defined using the cosine.

Image: NaturalLogarithmAll. png | Superposition of the previous 3 graphs

Two red graphs are duals for the blue one, but they are not Graph isomorphism | isomorphic.

The maximum number of edges is ½ | V | (| V |− 1 ), so the maximal density is 1 ( for complete graphs ) and the minimal density is 0.

Essentially, the graphs of antiderivatives of a given function are vertical translations of each other ; each graph's location depending upon the value of C.

Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

Some graphs are given for: 1N400x series, and CY7 cryogenic temperature sensor.

The graphs on the right side depict the ( finite ) coefficients that modulate the infinite amplitudes of a comb function whose teeth are spaced at the reciprocal of the time-domain periodicity.

This graph is planar ( it is important to note that we are talking about the graphs that have some limitations according to the map they are transformed from only ): it can be drawn in the plane without crossings by placing each vertex at an arbitrarily chosen location within the region to which it corresponds, and by drawing the edges as curves that lead without crossing within each region from the vertex location to each shared boundary point of the region.

: the problem of finding optimal colorings of graphs that are not necessarily planar.

: triangle-free planar graphs are 3-colorable.

Their motivations are consistent with the convictions of James Daniel Bjorken and Sidney Drell: ” The Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand.

Feynman diagrams are graphs that represent the trajectories of particles in intermediate stages of a scattering process.

The graphs on the right side depict the ( finite ) coefficients that modulate the infinite amplitudes of a comb function whose teeth are spaced at intervals of 1 / P.

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.

In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc.

Complementary to graph transformation systems focussing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.

More contemporary approaches such as Head-driven phrase structure grammar ( HPSG ) model syntactic constructions via the unification of typed feature structures, which are directed acyclic graphs.

Still other methods in phonology ( e. g. Optimality Theory, which uses lattice graphs ) and morphology ( e. g. finite-state morphology, using finite-state transducers ) are common in the analysis of language as a graph.

In mathematics, graphs are useful in geometry and certain parts of topology, e. g. Knot Theory.

Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values.

[...] I give a rule for the geometrical multiplication of graphs, i. e. for constructing a graph to the product of in-or co-variants whose separate graphs are given.

There are different ways to store graphs in a computer system.

List structures are often preferred for sparse graphs as they have smaller memory requirements.

Another class of problems has to do with the extent to which various species and generalizations of graphs are determined by their point-deleted subgraphs, for example: