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On the number of spanning trees in a graph
the mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph
Kirchhoff's_theorem
German physicist and mathematician (1824–1887)
another temperature. Kirchhoff also worked in the mathematical field of graph theory, in which he proved Kirchhoff's matrix tree theorem. Gesammelte Abhandlungen
Gustav_Kirchhoff
Topics referred to by the same term
radiation Kirchhoff equations in fluid dynamics Kirchhoff's three laws of spectroscopy Kirchhoff's law of thermochemistry Kirchhoff's theorem about the
Kirchhoff's_laws
Method to solve scalar wave equation
The Kirchhoff integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) is a surface integral to obtain the value of the solution
Kirchhoff_integral_theorem
Two equalities that deal with the current and potential difference
Lumped matter discipline Tellegen's Theorem Oldham, Kalil T. Swain (2008). The doctrine of description: Gustav Kirchhoff, classical physics, and the "purpose
Kirchhoff's_circuit_laws
Surname list
Gustav Kirchhoff Kirchhoff's theorem, in graph theory, a theorem concerning the number of "spanning trees" in a graph, named for Gustav Kirchhoff Kirchhof
Kirchhoff
Matrix representation of a graph
The Laplacian matrix relates to many functional graph properties. Kirchhoff's theorem can be used to calculate the number of spanning trees for a given
Laplacian_matrix
combination for each tree. The Markov chain tree theorem is closely related to Kirchhoff's theorem on counting the spanning trees of a graph, from which
Markov_chain_tree_theorem
theorem (combinatorics) Halpern–Läuchli theorem (Ramsey theory) Hindman's theorem (Ramsey theory) Kirchhoff's theorem (graph theory) Kneser's theorem
List_of_theorems
Theorem in network theory
Tellegen's theorem gives a simple relation between magnitudes that satisfy Kirchhoff's laws of electrical circuit theory. The Tellegen theorem is applicable
Tellegen's_theorem
Theorem in electrical circuit analysis
cases be more convenient than use of Kirchhoff's circuit laws. Various proofs have been given of Thévenin's theorem. Perhaps the simplest of these was the
Thévenin's_theorem
Physics formula
the Fresnel–Kirchhoff diffraction formula. Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's
Kirchhoff's diffraction formula
Kirchhoff's_diffraction_formula
Formula in graph theory
f = t(G) counting the number of spanning trees of a graph (also see Kirchhoff's theorem). It was later found that the flow polynomial is yet another; and
Deletion–contraction_formula
Area of discrete mathematics
degrees of the vertices, and is useful in some calculations such as Kirchhoff's theorem on the number of spanning trees of a graph. The distance matrix,
Graph_theory
Tree which includes all vertices of a graph
the determinant of a matrix derived from the graph, using Kirchhoff's matrix-tree theorem. Specifically, to compute t(G), one constructs the Laplacian
Spanning_tree
Statement on equilibrium in electromagnetism
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic
Earnshaw's_theorem
Theorem in physics showing the conservation of energy for the electromagnetic field
In electrodynamics, Poynting's theorem is a statement of conservation of energy for electromagnetic fields that was developed by British physicist John
Poynting's_theorem
Process of creating equivalent circuits
Miller theorem with regards to impedance supplied by two current sources connected in parallel. The two versions are based on the two Kirchhoff's circuit
Miller_theorem
Electrical engineering theorem
Millman's theorem (or the parallel generator theorem) is a method to simplify the solution of a circuit. Specifically, Millman's theorem is used to compute
Millman's_theorem
Statistical physics theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem to produce a method applicable to acoustics, seismology
Kirchhoff–Helmholtz_integral
Theorems describing elastic materials
Castigliano's theorems do not apply to 2 − D {\displaystyle 2-D} and 3 − D {\displaystyle 3-D} problems. The exception is the Kirchhoff plate, m = 2
Castigliano's_method
Model for a random simple path
explorer. Finally there is another link that should be mentioned: Kirchhoff's theorem relates the number of spanning trees of a graph G to the eigenvalues
Loop-erased_random_walk
Circuit theorem
The Extra Element Theorem (EET) is an analytic technique developed by R. D. Middlebrook for simplifying the process of deriving driving point and transfer
Extra_element_theorem
Foundational law of electromagnetism relating electric field and charge distributions
as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the
Gauss's_law
Theorem in classical electromagnetism
classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources)
Reciprocity (electromagnetism)
Reciprocity_(electromagnetism)
Assemblage of connected electrical elements
product of the resistance and the current flowing through it. Norton's theorem: Any network of voltage or current sources and resistors is electrically
Electrical_network
Thermal electromagnetic radiation
freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal amount of energy in each
Black-body_radiation
Vector calculus formulas relating the bulk with the boundary of a region
mathematician George Green, who discovered Green's theorem. This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using
Green's_identities
applied to trigonometry. There is evidence of an early form of Rolle's theorem in his work, though it was stated without a modern formal proof. In his
History_of_calculus
Association of electrical terms into pairs based on interchanging voltage and current
short circuit – open circuit Kirchhoff's current law (KCL) – Kirchhoff's voltage law (KVL) Thévenin's theorem – Norton's theorem The use of duality in circuit
Duality_(electrical_circuits)
German polymath and scholar (1777–1855)
Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence
Carl_Friedrich_Gauss
Cederbaum's theorem defines hypothetical analog electrical networks which will automatically produce a solution to the minimum s–t cut problem. Alternatively
Cederbaum's maximum flow theorem
Cederbaum's_maximum_flow_theorem
and the current flowing through it, at constant temperature. Norton's theorem: Any two-terminal collection of voltage sources and resistors is electrically
Mathematical methods in electronics
Mathematical_methods_in_electronics
German mathematician (1811–1874)
form, the Hesse configuration, the Hessian group, Hessian pairs, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many
Otto_Hesse
Law of electrical current and voltage
Maximum power transfer theorem Norton's theorem Electric power Sheet resistance Superposition theorem Thermal noise Thévenin's theorem Uses LED-Resistor circuit
Ohm's_law
Spectral density of light emitted by a black body
appropriate use of Planck's law. Classical physics led, via the equipartition theorem, to the ultraviolet catastrophe, a prediction that the total blackbody
Planck's_law
Method of analysis applied to problems wave propagation
1882, Gustav Kirchhoff analyzed Fresnel's theory in a rigorous mathematical formulation, as an approximate form of an integral theorem. Very few rigorous
Huygens–Fresnel_principle
Idealized physical body that absorbs all incident electromagnetic radiation
are an example of an interacting boson gas, and as described by the H-theorem, under very general conditions any interacting boson gas will approach
Black_body
Theorem in fluid mechanics
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from a hole to the height of
Torricelli's_law
Textbook for the Electronics Technician distance education program
structure, Kirchhoff's laws, energy, power, introductory circuit analysis techniques, Thevenin's theorem, the maximum power transfer theorem, electric
Principles_of_Electronics
dissipation theorem Helmholtz motion Helmholtz reciprocity Helmholtz resonance Helmholtz theorem (classical mechanics) Generalized Helmholtz theorem Helmholtz's
List of things named after Hermann von Helmholtz
List_of_things_named_after_Hermann_von_Helmholtz
Measure of directional electromagnetic energy flux
vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy
Poynting_vector
German mathematician (1821–1881)
hypergeometric series Andréief–Heine identity Heine theorem Heine–Borel theorem Heine–Cantor theorem Heine definition of continuity Heine's Reciprocal Square
Eduard_Heine
Basic law of electromagnetism
time t. It can also be written in an integral form by the Kelvin–Stokes theorem: ∮ ∂ Σ E ⋅ d l = − ∬ Σ ∂ B ∂ t ⋅ d A {\displaystyle \oint _{\partial \Sigma
Faraday's_law_of_induction
German mathematician (1823–1891)
theory he formulated the Kronecker–Weber theorem, without however offering a definitive proof (the theorem was proved completely much later by David
Leopold_Kronecker
French mathematician, physicist, and philosopher (1776–1831)
Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds
Sophie_Germain
English chemist and physicist (1791–1867)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Michael_Faraday
Number of spanning trees of a complete graph
formula are known. One classical proof of the formula uses Kirchhoff's matrix tree theorem, a formula for the number of spanning trees in an arbitrary
Cayley's_formula
Electric and magnetic fields produced by moving charged objects
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electromagnetic_field
Difference in electric potential between two points in space
between B and C. The various voltages in a circuit can be computed using Kirchhoff's circuit laws. When talking about alternating current (AC) there is a
Voltage
Representation of mechanical stress at every point within a deformed 3D object
that point. However, according to Cauchy's fundamental theorem, also called Cauchy's stress theorem, merely by knowing the stress vectors on three mutually
Cauchy_stress_tensor
Electric current that periodically reverses direction
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Alternating_current
Study of still or slow electric charges
or λ d ℓ {\displaystyle \lambda \,\mathrm {d} \ell } . The divergence theorem allows Gauss's law to be written in differential form: ∇ ⋅ E = ρ ε 0 .
Electrostatics
SI derived unit of power
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Watt
Flow of electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electric_current
Phenomena related to electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electricity
Production of voltage by a varying magnetic field
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electromagnetic_induction
French telegraph engineer (1857–1926)
circuits. As a result of studying Kirchhoff's circuit laws and Ohm's law, he developed his famous theorem, Thévenin's theorem, which made it possible to calculate
Léon_Charles_Thévenin
Types of electrical circuits
of the currents through the individual components, in accordance with Kirchhoff's current law. In a parallel circuit, the voltage is the same for all elements
Series_and_parallel_circuits
Charge transfer due to contact or sliding
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Triboelectric_effect
Rate at which electrical energy is transferred by an electric circuit
representation is often called the power triangle. Using the Pythagorean theorem, the relationship among real, reactive and apparent power is: (apparent
Electric_power
Electromagnetic property of matter
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electric_charge
French mathematician and physicist (1781–1840)
in systems of algebraic equations. Poisson gave a simplified proof of a theorem by Bézout on algebraic curves. In 1820 Poisson studied integrations along
Siméon_Denis_Poisson
the magnetic field would go with it. The theorem describing this effect is called the frozen-in-field theorem. Even in a fluid with a finite conductivity
Earth's_magnetic_field
Generalized function whose value is zero everywhere except at zero
Fourier integrals. Gustav Kirchhoff employed it in a paper applying Green's theorem in wave optics (Huygens' principle). Kirchhoff, Hermann von Helmholtz
Dirac_delta_function
Scientific study of digital information
of the channel noise. Shannon's main result, the noisy-channel coding theorem, showed that, in the limit of many channel uses, the rate of information
Information_theory
Principle in optics relating light rays and their reverse rays
electromagnetic nature of light became known. The Helmholtz reciprocity theorem has been rigorously proven in a number of ways, generally making use of
Helmholtz_reciprocity
German mathematician (1804–1851)
number theory, for example proving Fermat's two-square theorem and Lagrange's four-square theorem, and similar results for 6 and 8 squares. His other work
Carl_Gustav_Jacob_Jacobi
Italian chemist and physicist (1745–1827)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Alessandro_Volta
Electrical conductivity with exactly zero resistance
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Superconductivity
Imbalance of electric charges within or on the surface of a material
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Static_electricity
Physical model of propagating energy
superposed on the original wave fields, slow the wave (Ewald–Oseen extinction theorem). The amount of slowing depends on the electromagnetic properties of the
Electromagnetic_radiation
Closed loop path containing a magnetic flux
\mathbf {H} \cdot \mathop {} \!\mathrm {d} {\boldsymbol {l}}.} By Stokes's theorem, the closed line integral of H ⋅ d l {\displaystyle \mathbf {H} \cdot
Magnetic_circuit
Concept in classical electromagnetism
form". The forms are exactly equivalent, and related by the Kelvin–Stokes theorem (see the "proof" section below). Forms using SI units, and those using
Ampère's_circuital_law
Matrix that shows the relationship between two classes of objects
related to the adjacency matrix of its line graph L(G) by the following theorem: A ( L ( G ) ) = B ( G ) T B ( G ) − 2 I m . {\displaystyle A(L(G))=B(G)^{\textsf
Incidence_matrix
Technique in chemistry and manufacturing
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electrolysis
Electromagnetic effect in physics
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Hall_effect
Austrian mathematician and theoretical physicist (1844–1906)
law of thermodynamics using his gas-dynamical equation – his famous H-theorem. However the key assumption he made in formulating the collision term was
Ludwig_Boltzmann
Foundational law of classical magnetism
and an integral form. These forms are equivalent due to the divergence theorem. The name "Gauss's law for magnetism" is not universally used. The law
Gauss's_law_for_magnetism
Indian-American mathematician
the schemes defined by Kirchhoff polynomials to the representation spaces of matroids. Moreover, using Mnev's universality theorem, we show that these schemes
Prakash_Belkale
Unidirectional flow of electric charge
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Direct_current
Electrically insulating substance able to be polarised by an applied electric field
write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product, P ( ω ) = ε 0 χ e ( ω ) E ( ω )
Dielectric
British mathematical physicist (1793–1841)
published in 1828. In this essay he introduced an early version of Green's theorem in vector calculus, the notion of potential functions as currently used
George_Green_(mathematician)
Matroid that can be represented over all fields
computed as the determinant of an associated matrix, generalizing Kirchhoff's matrix-tree theorem for graphic matroids. The uniform matroid U 4 2 {\displaystyle
Regular_matroid
Discrete (i.e., incremental) version of infinitesimal calculus
These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with their
Discrete_calculus
Force acting on charged particles in electric and magnetic fields
as an approximation to the quantum dynamics: according to the Ehrenfest theorem, the expectation value of the momentum operator evolves according to an
Lorentz_force
Concept in graph theory
following have been proven: Jaeger's 4-flow Theorem. Every 4-edge-connected graph has a 4-flow. Seymour's 6-flow Theorem. Every bridgeless graph has a 6-flow
Nowhere-zero_flow
Surface integral of the magnetic field
the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as: Φ B = ∮ ∂ S A ⋅ d
Magnetic_flux
Electronic current integrator
capacitance of the cable Obtaining virtual zero impedance by applying Miller theorem Charge Transfer Amplifier Transducers with Charge Output "Piezoelectric
Charge_amplifier
Fundamental interaction between charged particles
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electromagnetism
sum needs to be accounted for. Eq. 2 is used to derive the distortion theorem which states that the more the individual bond lengths in a coordination
Bond_valence_method
German physicist (1857–1894)
cities of Dresden, Munich, and Berlin, where he studied under Gustav Kirchhoff and Hermann von Helmholtz. In 1880, Hertz obtained his Ph.D. from the
Heinrich_Hertz
Equations describing classical electromagnetism
of the Gauss divergence theorem and the Kelvin–Stokes theorem. According to the (purely mathematical) Gauss divergence theorem, the electric flux through
Maxwell's_equations
British chemist and inventor (1778–1829)
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Humphry_Davy
German mathematician (1844–1921)
theorem Noether's formula Noether inequality Noether's theorem on rationality for surfaces Max Noether's fundamental theorem Max Noether's theorem on
Max_Noether
Law Field Person(s) Named After Abel's theorem Calculus Niels Henrik Abel Ariadne's thread Computer science Ariadne Amdahl's law Computer science Gene
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Opposition to the passage of an electric current
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electrical resistance and conductance
Electrical_resistance_and_conductance
Object or material which allows the flow of electric charge with little energy loss
equations Displacement current Electromagnetic field Lorentz force Helmholtz theorem Retarded potentials Liénard–Wiechert potential Jefimenko's equations Radiation
Electrical_conductor
Analysis in fluid dynamics
loss Darcy–Weisbach equation Hazen–Williams equation Max-flow min-cut theorem Network theory S.H. Waldrip, R.K. Niven, M. Abel, M. Schlegel (2016), Maximum
Pipe_network_analysis
KIRCHHOFFS THEOREM
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