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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
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
Property of some mathematical operations
Commutative diagram Commutative (neurophysiology) Commutator Commuting graph Commuting probability Particle statistics (for commutativity in physics)
Commutative_property
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
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
. 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
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)
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
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
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
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
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
Computer compiler optimization technique
register allocation), or across function boundaries traversed via call-graph (interprocedural register allocation). When done per function/procedure
Register_allocation
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
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
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
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
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
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)
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
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)
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)
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
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
Computer algebra system
polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate
Cadabra_(computer_program)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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)
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
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)
Pilot certification
Why the U.S. Is Running Out of Pilots". Retrieved November 22, 2023. "CommuteAir • CommutAir Partners with ATP Flight School for Fast-Track Program"
Pilot certification in the United States
Pilot_certification_in_the_United_States
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
President of the United States (2017–2021; since 2025)
transferred to the Wharton School of the University of Pennsylvania, most often commuting to his father's office on weekends, and graduated in May 1968 with a Bachelor
Donald_Trump
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
Protests in India against three farm acts
staged protests to make farmers vacate the sites as it affected their commute. They also accused the farmers for disrespecting the Indian flag at Red
2020–2021 Indian farmers' protest
2020–2021_Indian_farmers'_protest
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
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
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 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
algebras, planar graphs, tilings, and rectangulations. Baxter introduced Baxter permutations while studying the fixed points of commuting continuous functions
Baxter_permutation
provost in 2001. Faudree specialized in combinatorics, and specifically in graph theory and Ramsey theory. He published more than 200 mathematical papers
Ralph_Faudree
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
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
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
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
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)
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
American multinational technology company
The Wall Street Journal. Retrieved January 14, 2022. "Five year history graph of (NASDAQ:MSFT) stock". ZenoBank. AlphaTrade. September 29, 2009. Archived
Microsoft
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
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
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
Mathematics of number-placement puzzle
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
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
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)
Theory of quantum gravity merging quantum mechanics and general relativity
appropriate to non-graph-changing operators, however, Thiemann's Hamiltonian constraint is a graph-changing operator – the new graph it generates has degrees
Loop_quantum_gravity
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
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
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
American conservative political commentator (born 1969)
Graziosi, Graig (December 17, 2021). "Tucker Carlson mocked for using wrong graph to falsely complain women outnumber men in US workforce". The Independent
Tucker_Carlson
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
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
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
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
On the existence of arithmetic progressions in subsets of the natural numbers
Hillel; Katznelson, Yitzhak (1978). "An ergodic Szemerédi theorem for commuting transformations". Journal d'Analyse Mathématique. 38 (1): 275–291. doi:10
Roth's theorem on arithmetic progressions
Roth's_theorem_on_arithmetic_progressions
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
Theory in statistics
symmetric association scheme can be visualized as a complete graph with labeled edges. The graph has v {\displaystyle v} vertices, one for each point of X
Association_scheme
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
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
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)
Capital and most populous city in Japan
daytime, the population swells by over 2.5 million as workers and students commute from adjacent areas. This effect is even more pronounced in the three central
Tokyo
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
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
Reservoir in Virginia, United States
Mountain Lake Regional Chamber of Commerce SML Dam website (Appalachian Power) Graph of SML water levels, tracked by hour (donation-based website) Smith Mountain
Smith_Mountain_Lake
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
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
Most populous city in Oregon, U.S.
bicycle-friendly cities in the world. Bicycles accounted for 3.2% of commuting in 2024. Bicycle commuting declined by 46% between 2016 and 2022 according to Portland
Portland,_Oregon
Most populous city in Pennsylvania, US
many affluent residents to depart the city for its outlying railroad commuting towns and newer housing. The resulting reduction in Philadelphia's tax
Philadelphia
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
Mathematical function
dimensions, in Cartesian and spherical geometry, on surfaces and in volumes, on graphs, and in scalar, vector, and tensor forms. Without reference to any of these
Slepian_function
Post-quantum cryptographic algorithm
Diffie–Hellman key exchange, but is based on walks in a supersingular isogeny graph and was designed to resist cryptanalytic attack by an adversary in possession
Supersingular isogeny key exchange
Supersingular_isogeny_key_exchange
Chinese-American mathematician (born 1949)
book "Spectral Graph Theory". Later, they introduced a Green's function as defined for graphs, amounting to a pseudo-inverse of the graph Laplacian.[CY00]
Shing-Tung_Yau
COMMUTING GRAPH
COMMUTING GRAPH
Boy/Male
Spanish American Italian Latin
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...
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...
COMMUTING GRAPH
COMMUTING GRAPH
Boy/Male
Arabic, Muslim
The Governor; He who Directs; Manages; Conducts; Measure
Girl/Female
Arabic, Muslim
A Poem of Six Verses
Boy/Male
Indian
Fullmoon Richness of Lakshmi
Girl/Female
Hindu
The cuckoo bird
Girl/Female
Hindu
Life
Biblical
full of grace
Boy/Male
Indian
Refreshment, Rest
Boy/Male
Indian
Respectable Man, Intelligent
Boy/Male
Australian, Polish
Fame
Girl/Female
Australian, Finnish, Hebrew
Friend; Companion
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
COMMUTING GRAPH
n.
The act or process of commenting or criticising; exposition.
v. i.
To make an enumeration or computation; to engage in numbering or computing.
a.
Acting in competition; competing; rival.
p. pr. & vb. n.
of Combat
a.
Engaged in warfare; fighting; combating; serving as a soldier.
p. pr. & vb. n.
of Compute
p. pr. & vb. n.
of Comment
p. pr. & vb. n.
of Compete
n.
The act or process of computing; calculation; reckoning.
p. pr. & vb. n.
of Commune
p. pr. & vb. n.
of Commute
n.
A contrivance for computing the revolutions of a wheel; an odometer.
p. pr. & vb. n.
of Commit
p. pr. & vb. n.
of Comminute
p. pr. & vb. n.
of Confute
p. pr. & vb. n.
of Commove
p. pr. & vb. n.
of Commix
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 confuting; refutation.
a.
Having the character of larceny; as, a larcenous act; committing larceny.