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In mathematics, the commuting graph of a semigroup, or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup
Commuting_graph
Property of some mathematical operations
Commutative diagram Commutative (neurophysiology) Commutator Commuting graph Commuting probability Particle statistics (for commutativity in physics)
Commutative_property
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Type of graph in mathematical graph theory
n/3)-lollipop graphs are known to be graphs which achieve the maximum possible hitting time, cover time and commute time. Barbell graph Tadpole graph Weisstein
Lollipop_graph
Mathematical group based upon a finite number of elements
theorem (group theory) Classification of finite simple groups Commuting graph Commuting probability Finite ring Finite-state machine Infinite group List
Finite_group
the isomorphism Z6 ≅ Z3 × Z2. Chen, Jing; Tang, Lang (2020). "The Commuting Graphs on Dicyclic Groups". Algebra Colloquium. 27 (4): 799–806. doi:10
List_of_small_groups
Theorem classifying finite simple groups
xn = 1. Non-abelian finite simple groups are characterized by their commuting graphs. O'Nan–Scott theorem Rose Eveleth (2011-12-09). "The Funniest Theories
Classification of finite simple groups
Classification_of_finite_simple_groups
Graph structure studied in group theory
cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are
Cycle_graph_(algebra)
Undirected graph defined from a group
In the mathematics of graph theory and finite groups, a prime graph is an undirected graph defined from a group. These graphs were introduced in a 1981
Prime_graph
Topics referred to by the same term
music videos by Miki Nakatani, 1998 Complete set of commuting operators (or CSCO), a set of commuting operators in quantum mechanics whose eigenvalues are
Completeness
Graph metric of electrical resistance between nodes
In graph theory, the resistance distance between two vertices of a simple, connected graph, G, is equal to the resistance between two equivalent points
Resistance_distance
. A different choice of commuting squares can yield a distinct k {\displaystyle k} -graph with the same skeleton. A 1-graph is precisely the path category
K-graph_C*-algebra
Pictorial representation of the behavior of subatomic particles
device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, because the path integral was unfamiliar when
Feynman_diagram
3-transpositions all commuting with one another has size 22 and is called a basic set. There are 1024 3-transpositions, called anabasic that do not commute with any
Fischer_group
Concept in quantum computing
computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there
Graph_state
Periodic spatial graph
Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three
Laves_graph
In mathematics, a fibration of graphs, or graph fibration, is a homomorphism of directed graphs that satisfies a unique lifting property analogous to that
Fibrations_of_graphs
Computer compiler optimization technique
register allocation), or across function boundaries traversed via call-graph (interprocedural register allocation). When done per function/procedure
Register_allocation
Mathematical function, denoted exp(x) or e^x
algebras. The graph of y = e x {\displaystyle y=e^{x}} is upward-sloping, and increases faster than every power of x {\displaystyle x} . The graph always
Exponential_function
figure to the right shows the commuting diagram for program p3 = i+j+h = [g3,s3,b3]. A fundamental property of a commuting diagram is that all paths between
Feature-oriented_programming
Paradox related to increasing roadway capacity
reduction of the road network, which may cause a reduction of individual commuting time. In Seoul, South Korea, traffic around the city sped up when the
Braess's_paradox
generating set. The graph is connected and vertex transitive. Paths in the graph correspond to words in the generators. If the graph has a cycle of a given
Thin group (combinatorial group theory)
Thin_group_(combinatorial_group_theory)
Association of one output to each input
is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the
Function_(mathematics)
States that the algebra of n by n matrices satisfies a certain identity of degree 2n
S_{n}}{\text{sgn}}(\sigma )x_{\sigma (1)}\cdots x_{\sigma (n)}} in non-commuting variables x1, ..., xn, where the sum is taken over all n! elements of
Amitsur–Levitzki_theorem
Mathematical problem solved in 1967
points of commuting functions. Building on earlier work by J. F. Ritt and A. G. Walker, Block and Thielman identified sets of pairwise commuting polynomials
Common_fixed_point_problem
Optimization algorithms using quantum computing
problem. The mixer Hamiltonian is the simple, non-commuting sum of Pauli-X operations on each node of the graph and they are given by: H C = − 0.25 Z 3 + 0
Quantum optimization algorithms
Quantum_optimization_algorithms
City in Giza, Egypt
people from within the city and other parts of Giza (as well as those commuting further from surrounding regions). Some of the largest businesses with
6th_of_October_(city)
Directed graph which is also a multigraph
theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers
Quiver_(mathematics)
Operation in graph theory
In graph theory, local complementation (also known as vertex inversion) is an operation on a graph that toggles adjacencies among the neighbours of a
Local_complementation
travel information for driving in the United States. "Who Drives to Work? Commuting by Automobile in the United States: 2013". Census.gov. United States Census
Driving_in_the_United_States
Slovak-German computer scientist (born 1979)
University of Cologne. Her research concerns information visualization, graph drawing, and visual analytics. Von Landesberger was born in 1979 in Bratislava
Tatiana_von_Landesberger
Context dependence in quantum measurements
(assumed pre-existing) of a quantum observable is dependent upon which other commuting observables are within the same measurement set. Contextuality was first
Quantum_contextuality
Computer algebra system
polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate
Cadabra_(computer_program)
16-element matrix group
quantum error correction codes using sets of commuting Pauli operators. Stabilizer codes are formed from commuting subgroups of the Pauli group. The Pauli
Pauli_group
group-theoretic symmetry through automorphisms. It is based on the theory of graph fibrations and provides a natural framework for understanding robust cluster
Fibration_symmetry
Reversal of the order of elements of a binary relation
f^{-1}\subseteq Y\times X} defined by the graph f − 1 = { ( y , x ) ∈ Y × X : y = f ( x ) } . {\displaystyle \operatorname {graph} \,f^{-1}=\{(y,x)\in Y\times X:y=f(x)\}
Converse_relation
Largest absolute value of an operator's eigenvalues
radius of a product of commuting matrices: if A 1 , … , A n {\displaystyle A_{1},\ldots ,A_{n}} are matrices that all commute, then ρ ( A 1 ⋯ A n ) ≤
Spectral_radius
Pictorial representation of symmetry
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter
Coxeter–Dynkin_diagram
Group that admits a formal description in terms of reflections
In particular, two generators commute if and only if they are not joined by an edge. Furthermore, if a Coxeter graph has two or more connected components
Coxeter_group
Type of continuous map in topology
lattice is the universal cover of a Cayley graph Covering graph, a covering space for an undirected graph, and its special case the bipartite double cover
Covering_space
this way form the vertices of the principal graph, a bipartite graph. The directed edges of these graphs describe the way an irreducible bimodule decomposes
Subfactor
Conceptually, partial inversion corresponds to a rotation of the graph of the matrix ( X , A X ) ∈ V × V {\displaystyle (X,AX)\in V\times V} ,
Partial_inverse_of_a_matrix
Mathematical method in extremal graph theory
mathematics, the hypergraph regularity method is a powerful tool in extremal graph theory that refers to the combined application of the hypergraph regularity
Hypergraph_regularity_method
bipartite graphs. Degree matrix — a diagonal matrix defining the degree of each vertex in a graph. Edmonds matrix — a square matrix of a bipartite graph. Incidence
List_of_named_matrices
Type of proof technique
commonly proven with a double counting argument states that every undirected graph contains an even number of vertices of odd degree. That is, the number of
Double counting (proof technique)
Double_counting_(proof_technique)
Basic integral in elementary calculus
interval. It defines the integral by approximating the region under the graph of a function by finite sums of areas of vertical rectangles. For suitable
Riemann_integral
Mathematics construct
maps h : S → T {\displaystyle h:S\to T} that make the diagram commute. The category of graphs is ( S e t ↓ D ) {\displaystyle \scriptstyle {(\mathbf {Set}
Comma_category
provost in 2001. Faudree specialized in combinatorics, and specifically in graph theory and Ramsey theory. He published more than 200 mathematical papers
Ralph_Faudree
Expansion coefficients in statistical mechanics
irreducible graphs with one white and}}\ i\ {\mbox{black vertices}}} The rule for turning these graphs into integrals is as follows: Take a graph and label
Virial_coefficient
1997 film by Gus Van Sant
Lambeau on the blackboard. The problem has to do with intermediate-level graph theory, but Lambeau describes it as an advanced "Fourier system". To answer
Good_Will_Hunting
Polynomial in combinatorial mathematics
1}a_{2}+2a_{3}\right).} It happens that the complete graph K3 is isomorphic to its own line graph (vertex-edge dual) and hence the edge permutation group
Cycle_index
Place in East Sepik Province, Papua New Guinea
15 July 2011. Retrieved 6 June 2010. "Climate: Wewak – Climate graph, Temperature graph, Climate table". Climate-Data.org. Retrieved 18 December 2013.
Wewak
Property of a mathematical operation
Associative property A visual graph representing associative operations; ( x ∘ y ) ∘ z = x ∘ ( y ∘ z ) {\displaystyle (x\circ y)\circ z=x\circ (y\circ
Associative_property
Hand game for two players or more
22, 1932 - The New York Times Magazine, article by Marion May Dilts: "COMMUTING WITH TOKYO'S SUBURBANITES; Their Morning Ritual Is Characteristically
Rock_paper_scissors
Lecture series established by the Association for Women in Mathematics
2025 Neena Gupta The Abhyankar-Sathaye Conjecture for Linear Hyperplanes 2026 Monica Vișan Well-Posedness and the Method of Commuting Flows References:
Noether_Lecture
Mathematics concept
rank (given by 1 plus the Euler characteristic of the quotient graph). The Cayley graph of a free group of finite rank, with respect to a free generating
Free_group
Method of describing higher-order polyhedra
equivalent polyhedra can be thought of as one of many embeddings of a polyhedral graph on the sphere. Unless otherwise specified, in this article (and in the literature
Conway_polyhedron_notation
In general, exponentiation fails to be commutative
Archived from the original on 2021-08-15. Retrieved 2016-04-14. "x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived
Equation_xy_=_yx
City in Colorado, United States
Retrieved February 5, 2022. "Climate: Woodland Park - Climate graph, Temperature graph, Climate table - Climate-Data.org". En.climate-data.org. Retrieved
Woodland_Park,_Colorado
Pair of polynomial sequences
(bottom) the 5th partial sum of its Chebyshev expansion. The 7th sum is indistinguishable from the original function at the resolution of the graph.
Chebyshev_polynomials
Common mode of transport and sport
This graph was using the legacy Graph extension, which is no longer supported. It needs to be converted to the new Chart extension.
Cycling_in_the_Philippines
American information technology company (1939–2015)
programmable, expandable in 1979 (the HP-41C), and the first symbolic and graphing calculator, the HP-28C. Like its scientific and business calculators, HP
Hewlett-Packard
Canadian-American baseball player (born 1989)
2022. Hulet, Marc (September 8, 2009). "AFL preview: Peoria Saguaros". FanGraphs. Retrieved April 15, 2022. Curtright, Guy (April 7, 2010). "Freeman happy
Freddie_Freeman
Class of molecular symmetry
y , H ] = 0 {\displaystyle [{{A}_{y}},H]=0} . So the Complete Set of Commuting Operators (CSCO) for a general heteronuclear diatomic molecule is { H
Symmetry of diatomic molecules
Symmetry_of_diatomic_molecules
Matrix equal to its conjugate-transpose
often exhibit Hermitian properties. In graph theory, Hermitian matrices are used to study the spectra of graphs. The Hermitian Laplacian matrix is a key
Hermitian_matrix
Concept in incidence geometry
d {\displaystyle 2d} -gons whose point graph (also known as a collinearity graph) is a distance-regular graph. A generalized 2 d {\displaystyle 2d} -gon
Near_polygon
mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows
Free_category
Most general completion of a commutative square given two morphisms with same codomain
pullback is given by the graph of a function. Suppose that f : X → Y {\displaystyle f\colon X\to Y} is a function. The graph of f is the set Γ f = { (
Pullback_(category_theory)
Mathematical space with a notion of distance
mathematics. For example, Riemannian manifolds, normed vector spaces, and graphs may be viewed as metric spaces. In abstract algebra, the field of p-adic
Metric_space
German football manager (born 1973)
documentary on Pep Guardiola for two hours on the Mainz bus to study a graph which showed Barcelona's passing patterns. Tuchel has borrowed training
Thomas_Tuchel
Array of numbers
The adjacency matrix of a finite graph is a basic notion of graph theory. It records which vertices of the graph are connected by an edge. Matrices
Matrix_(mathematics)
Method of quantum computing
first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because
One-way_quantum_computer
Four finite groups derived from the Leech lattice
Hall–Janko group HJ makes its appearance. The aforementioned graph expands to the Hall–Janko graph, with 100 vertices. Next comes (2.A4 o 2.G2(4)):2, G2(4)
Conway_group
Hypothetical event
evidence that it is likely or even possible. Look at domed cities, jet-pack commuting, underwater cities, mile-high buildings, and nuclear-powered automobiles—all
Technological_singularity
Mobile GPS navigation app
that the carpool app would be retired, citing COVID-related changes in commuting patterns that led to a sharp decline in carpooling. In November 2023,
Waze
Social bookmarking service
incredibly useful for saving all the articles and news stories I find while commuting or waiting in line." Erez Zukerman of PC World said that supporting the
Pocket_(service)
Mass Rapid Transit station in Singapore
a series of line-drawings by Ian Woo, while the CCL platforms feature Commuting Waves by Jason Ong and a set of art seats entitled Matrix. In preliminary
HarbourFront_MRT_station
Capital and largest city in Hawaii, US
Honolulu residents commuted to work by driving alone, 13.8% carpooled, 11.7% used public transportation, and 8.7% walked. About 5.7% commuted by bike, taxi
Honolulu
Mathematical investigation of Sudoku
variation of graph coloring with some graph vertices already starting with assigned colors. The aim is to construct a 9-coloring of a particular graph, given
Mathematics_of_Sudoku
Generalization of strings in computer science
computation, where commuting letters stand for portions of a job that can execute independently of one another, while non-commuting letters stand for locks
Trace_monoid
Computer science concept
ordering is sufficient for consistency when transactions do not conflict. Graph-based dependency models, such as those utilized in the Cerberus protocol
State_machine_replication
City in California, United States
significant number of people have moved to adjacent Riverside County, commuting daily to jobs in San Diego, while others are leaving the area altogether
San_Diego
UK Parliament constituency (1997–2024)
popular with kayakers and part of the Blackdown Hills). Some residents commute to Exeter. Residents' wealth is around average for the UK. 1997–2010: The
Tiverton_and_Honiton
Map that depicts the area accessible from a point within a time threshold
currently typically computed by via generating shortest-path trees on network graphs, and then generating a convex hull around the accessible nodes. Increases
Isochrone_map
extraordinary unpopularity of Trump's family separation policy (in one graph)". The Washington Post. ISSN 0190-8286. Retrieved June 20, 2018. Alexander
Domestic policy of the first Trump administration
Domestic_policy_of_the_first_Trump_administration
Theorem in linear algebra
theorem has particular use in algebraic graph theory. The "underlying graph" of a nonnegative n-square matrix is the graph with vertices numbered 1, ..., n and
Perron–Frobenius_theorem
lowest percentage of residents commuting out-of-county to work. Only Brown County residents were less likely to commute out of their county to work. 89
Economy of Door County, Wisconsin
Economy_of_Door_County,_Wisconsin
Shape in the geometry of numbers
sail V {\displaystyle \textstyle V} of an irrational cone are two graphs: the graph Γ e ( V ) {\displaystyle \textstyle \Gamma _{\mathrm {e} }(V)} whose
Klein_polyhedron
Battery electric subcompact car
and MINI E vehicles in Asia, Europe and the U.S., whereby the typical commuting use between the pilot users' homes and workplaces was calculated. The
BMW_i3_(hatchback)
Element of a unital algebra over the field of real numbers
set { e 0 , e 1 } {\displaystyle \{e_{0},\,e_{1}\}} of mutually anti-commuting elements of A {\displaystyle A} such that e 0 2 = e 1 2 = − 1 {\displaystyle
Hypercomplex_number
Town in Auckland, New Zealand
(Auckland)". www.intercity.co.nz. Retrieved 27 September 2018. "Luxury Commuting On eCoaches. Round-Trip Bus From Auckland to Warkworth". Mahu City Express
Warkworth,_New_Zealand
Quantum physics-based metaheuristic for optimization problems
(the original function + non-commuting part) just as described above. Here, there is a choice in selecting the non-commuting term and the efficiency of
Quantum_annealing
Multi-dimensional generalization of triangle
Hasse diagram of the face lattice of an n-simplex is isomorphic to the graph of the (n + 1)-hypercube's edges, with the hypercube's vertices mapping
Simplex
Capital of Colorado, U.S.
mile of most of its residents. The average amount of time people spend commuting on public transit in Denver and Boulder, Colorado—for example, to and
Denver
American dark comedy-drama film by Sam Mendes
handgun from the glove box as she listens to a self-help tape during her commute. At home, Jane argues with Lester and Angela over Angela's sexual interest
American_Beauty_(1999_film)
with only a trace of precipitation for the entire month. See or edit raw graph data. Some palm trees like palmetto and cacti like prickly pear can withstand
Geography_of_Atlanta
Discrete (i.e., incremental) version of infinitesimal calculus
velocity of the ball. If a function is linear (that is, if the points of the graph of the function lie on a straight line), then the function can be written
Discrete_calculus
President of South Korea since 2025
Franklin D. Roosevelt. On 10 October 2021, Lee said "We will change the graph of economic growth upward with a strong state-led economic revival policy
Lee_Jae_Myung
Extended and increasing shortage since 1970
would have five times the population it has today. In 2023, CalMatters graphed the various estimates of the housing shortage against actual housing production
California_housing_shortage
Theories in mathematical logic
language of graphs.) The theory of random graphs is ω categorical, complete, and decidable, and its countable model is called the Rado graph. A statement
List_of_first-order_theories
COMMUTING GRAPH
COMMUTING GRAPH
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
COMMUTING GRAPH
COMMUTING GRAPH
Girl/Female
Norse
The tree that binds heaven hell and earth.
Boy/Male
Hindu, Indian
God Place
Girl/Female
Tamil
Surname or Lastname
German and Dutch
German and Dutch : from a pet form of the personal name Thomas.English : unexplained.
Boy/Male
Indian, Punjabi, Sikh
Brave in the Battlefield
Girl/Female
Tamil
Annjaya | அநà¯à®¨à¯à®œà®¯
Unique
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Telugu, Traditional
A Very Beautiful Woman
Boy/Male
Arabic, Indian, Marathi, Muslim
Moon Light
Surname or Lastname
English (West Midlands)
English (West Midlands) : unexplained.German : variant of Roden.
Girl/Female
Indian
Keeper of the sacred book, Successful
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
p. pr. & vb. n.
of Commit
p. pr. & vb. n.
of Compete
p. pr. & vb. n.
of Comment
a.
Having the character of larceny; as, a larcenous act; committing larceny.
a.
Acting in competition; competing; rival.
p. pr. & vb. n.
of Commove
p. pr. & vb. n.
of Commute
p. pr. & vb. n.
of Commix
p. pr. & vb. n.
of Combat
p. pr. & vb. n.
of Confute
a.
Engaged in warfare; fighting; combating; serving as a soldier.
p. pr. & vb. n.
of Commune
n.
The act or process of confuting; refutation.
p. pr. & vb. n.
of Comminute
p. pr. & vb. n.
of Compute
v. i.
To make an enumeration or computation; to engage in numbering or computing.
n.
The act or process of computing; calculation; reckoning.
n.
A contrivance for computing the revolutions of a wheel; an odometer.
n.
The act of committing, or putting in charge, keeping, or trust; consignment; esp., the act of committing to prison.
n.
The act or process of commenting or criticising; exposition.