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Graph where any two induced paths between nodes both have odd or even lengths
In graph theory, a parity graph is a graph in which all induced paths between the same two vertices have the same parity: either all paths have odd length
Parity_graph
Graph with tight clique-coloring relation
parity. The prism over any parity graph (its Cartesian product with a single edge) is another parity graph, and the parity graphs are the only graphs
Perfect_graph
Largest independent set of paired elements
generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Matroid parity can be solved
Matroid_parity_problem
Linear error correcting code
Low-density parity-check (LDPC) codes, also known as Gallager codes, are a class of error-correction codes first proposed in 1960. Together with the closely
Low-density_parity-check_code
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Bipartite graph in coding theory
parity-check codes. They have also been applied to the construction of longer codes from smaller ones. Both encoders and decoders employ these graphs
Tanner_graph
Quality of zero being an even number
spoken articles) In mathematics, zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. This can be easily
Parity_of_zero
Graph formed by complementation and disjoint union
been called D*-graphs, hereditary Dacey graphs (after the related work of James C. Dacey Jr. on orthomodular lattices), and 2-parity graphs. They have a
Cograph
Graph whose line graph is perfect
perfect graphs themselves, every line perfect graph is itself perfect. By similar reasoning, every line perfect graph is a parity graph, a Meyniel graph, and
Line_perfect_graph
Property of being an even or odd number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For
Parity_(mathematics)
Mathematical game played on a directed graph
A parity game is played on a colored directed graph, where each node has been colored by a priority – one of (usually) finitely many natural numbers.
Parity_game
Complete bipartite cut in a graph
to recognize distance-hereditary graphs in linear time. Parity graphs can be recognized in linear time as the graphs in which each split quotient is either
Split_(graph_theory)
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges
Graph_minor
Machine learning framework for portfolio construction
Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners
Hierarchical_Risk_Parity
Open problem on 3x+1 and x/2 functions
If P(...) is the parity of a number, that is P(2n) = 0 and P(2n + 1) = 1, then we can define the Collatz parity sequence (or parity vector) for a number
Collatz_conjecture
Unsolved problem in computational complexity theory
X {\displaystyle X} . The graph isomorphism problem is contained in both NP and co-AM. GI is contained in and low for Parity P, as well as contained in
Graph_isomorphism_problem
Graph whose induced subgraphs preserve distance
graph is a perfect graph, more specifically a perfectly orderable graph and a Meyniel graph. Every distance-hereditary graph is also a parity graph,
Distance-hereditary_graph
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing
Parity_P
Help Desk. "This term is often used in conjunction with Purchasing Power Parity (PPP) data." "Full Report: Health at a Glance 2023: OECD Indicators". OECD
List of countries by total health expenditure per capita
List_of_countries_by_total_health_expenditure_per_capita
discusses sparse-graph codes in Chapters 47–50. Encyclopedia of Sparse Graph Codes Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Cccumulate
Sparse_graph_code
Graph whose biconnected components are all cliques
in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest
Block_graph
Graph where each vertex has the same number of neighbors
numbers satisfying both the inequality and the parity condition, then indeed there is a k-regular circulant graph C n s 1 , … , s r {\displaystyle C_{n}^{s_{1}
Regular_graph
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
Plot using the dispersal of scattered dots to show the relationship between variables
information visualization Rug plot Bar graph Line chart List of mathematical art software Scagnostics Dot plot (statistics) Parity plot Jarrell, Stephen B. (1994)
Scatter_plot
Classification of algorithm
impractical algorithm becomes practical. See, for example, low-density parity-check codes, below. An impractical algorithm can still demonstrate that
Galactic_algorithm
Sliding puzzle with fifteen pieces and one space
about the remaining half. The invariant is the parity of the permutation of all 16 squares plus the parity of the taxicab distance (number of rows plus
15_puzzle
Functions such that f(–x) equals f(x) or –f(x)
series Holstein–Herring method Parity (physics) Gel'Fand, I. M.; Glagoleva, E. G.; Shnol, E. E. (1990). Functions and Graphs. Birkhäuser. ISBN 0-8176-3532-7
Even_and_odd_functions
Topics referred to by the same term
generalized paths in matroids Hanani–Tutte theorem on the parity of edge crossings in graph drawings This disambiguation page lists articles associated
Tutte's_theorem
Mathematical graph relating to chess
mathematics, a queen's graph is an undirected graph that represents all legal moves of the queen—a chess piece—on a chessboard. In the graph, each vertex represents
Queen's_graph
Graph where all odd cycles of length ≥ 5 has 2+ chords
Meyniel graphs contain the chordal graphs, the parity graphs, and their subclasses the interval graphs, distance-hereditary graphs, bipartite graphs, and
Meyniel_graph
On parity of crossings in graph drawings
In topological graph theory, the Hanani–Tutte theorem is a result on the parity of edge crossings in a graph drawing. It states that every drawing in
Hanani–Tutte_theorem
mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100
Higman–Sims_graph
List of unsolved computational problems
time? Can parity games be solved in polynomial time? Can the rotation distance between two binary trees be computed in polynomial time? Can graphs of bounded
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Mathematical tree of cycles
in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest
Cactus_graph
Complexity class of problems
winner in parity games, in which graph vertices are labeled by which player chooses the next step, and the winner is determined by the parity of the highest-priority
NP-intermediate
NP-hard problem in combinatorial optimization
version of the TSP (where given a length L, the task is to decide whether the graph has a tour whose length is at most L) belongs to the class of NP-complete
Travelling_salesman_problem
Problem of finding a cycle through all vertices of a graph
theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly
Hamiltonian_path_problem
Complexity class
In computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD
PPAD_(complexity)
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Algorithm for statistical inference on graphical models
demonstrated empirical success in numerous applications, including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability
Belief_propagation
Communication interface transmitting information sequentially
Mark (M) parity means that the parity bit is always set to the mark signal condition (1 bit value). Space (S) parity always sends the parity bit in the
Serial_port
the graph. Similar to other graph measures, such as cycle rank, some algorithmic problems, e.g. parity game, can be efficiently solved on graphs of bounded
Entanglement_(graph_measure)
Obsolete unit of account of the European Community
replaced the European Unit of Account (EUA) at parity in 1979, and it was later replaced by the euro (EUR) at parity on 1 January 1999. As a unit of account
European_Currency_Unit
Variation of a finite automaton that runs on infinite input
ω-automata include the Büchi automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These
Ω-automaton
2018 mathematics book by Marcus Schaefer
the parity of crossings. The second chapter concerns other special classes of graphs including graph products (especially products of cycle graphs) and
Crossing_Numbers_of_Graphs
Algorithmically defined graph
In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented
Implicit_graph
Series of Casio graphing calculators
The Casio Algebra FX series was a line of graphing calculators manufactured by Japanese electronics company Casio Computer Co., Ltd from 1999 to 2003.
Casio_Algebra_FX_Series
Scheme for controlling errors in data over noisy communication channels
point-to-point links Long code Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes LT code, which is a near-optimal
Error_correction_code
Assignment problem in combinatorial mathematics
matching in a graph that has a vertex for every number in the range from 1 to 2n and an edge between every pair of numbers that has different parity and are
Ménage_problem
Vertices whose removal breaks all cycles
instance of the matroid parity problem for linear matroids. The special case of finding all feedback vertices in a directed graph (vertices that lie on
Feedback_vertex_set
Computational complexity class
the combined input and output size. Parity games, involving token-passing along the edges of a colored directed graph. The paper giving a quasi-polynomial
Quasi-polynomial_time
Unequal access to higher quality healthcare
This graph contrasts total health care spending with public spending, in US dollars adjusted for purchasing power parity in Switzerland.
Two-tier_healthcare
a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type
Universal_graph
be found in any graph in polynomial time, by a transformation to a more general computational problem on matroids, the matroid parity problem for linear
Xuong_tree
Data structure for Boolean functions
propositional directed acyclic graphs (PDAG). A Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several (decision)
Binary_decision_diagram
Isotope of hydrogen with one neutron
is symmetric under parity (i.e. has an "even" or "positive" parity), and antisymmetric if the deuteron is antisymmetric under parity (i.e. has an "odd"
Deuterium
Type of non-sinusoidal waveform
circuits at precisely determined intervals. However, as the frequency-domain graph shows, square waves contain a wide range of harmonics; these can generate
Square_wave_(waveform)
Probabilistic model
or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables
Graphical_model
Peruvian mathematician (born 1977)
of Henryk Iwaniec and Peter Sarnak, with the thesis Root numbers and the parity problem. Helfgott was a post-doctoral Gibbs Assistant Professor at Yale
Harald_Helfgott
Boolean variable on each edge of a planar graph, and if the variables of the edges incident to each vertex of the graph are constrained to belong to an even
Delta-matroid
Characterization of the size of a maximum matching in a graph
theorem. Graph toughness, a problem of creating many connected components by removing a small set of vertices without regard to the parity of the components
Tutte–Berge_formula
Type of radioactive decay
from 60 Co proved that parity is not conserved in beta decay. This surprising result overturned long-held assumptions about parity and the weak force. In
Beta_decay
Mathematical puzzle game
undirected graph, the nodes representing distributions of disks and the edges representing moves. For one disk, the graph is a triangle: The graph for two
Tower_of_Hanoi
All even-degree subgraphs of a graph
In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree spanning subgraphs, or the set
Cycle_space
Problem on triangles in graph theory
of graphs", Graphs and Combinatorics, 6 (4): 373–380, doi:10.1007/BF01787705, MR 1092587 Lawler, Eugene L. (1976), "Chapter 9: The Matroid Parity Problem"
Tuza's_conjecture
Absence of, or a violation of, symmetry
verified parity violation.[citation needed] After the discovery of the violation of parity in 1956–57, it was believed that the combined symmetry of parity (P)
Asymmetry
Implied volatility patterns that arise in pricing financial options
on the at-the-money (strike price near the underlying's forward price). Graphing implied volatilities against strike prices for a given expiry produces
Volatility_smile
Estimate of time taken for running an algorithm
Khoussainov, Bakhadyr and Li, Wei and Stephan, Frank (2017). "Deciding parity games in quasipolynomial time". Proceedings of the 49th Annual ACM SIGACT
Time_complexity
Radioactive isotope of cobalt
missing. In 1957, Chien-Shiung Wu et al. discovered that β-decay violated parity, implying nature (the weak force) sees handedness. In the Wu experiment
Cobalt-60
Inverse functions of sin, cos, tan, etc.
With the help of integer parity Parity ( h ) = { 0 if h is even 1 if h is odd {\displaystyle \operatorname {Parity} (h)={\begin{cases}0&{\text{if
Inverse trigonometric functions
Inverse_trigonometric_functions
Complexity class
theory, PPA is a complexity class, standing for "Polynomial Parity Argument" (on a graph). Introduced by Christos Papadimitriou in 1994 (page 528), PPA
PPA_(complexity)
Shared independent set of two matroids
matroids, the matroid parity problem, was formulated by Lawler as a common generalization of matroid intersection and non-bipartite graph matching. However
Matroid_intersection
Complexity class of bounded-depth circuits
hierarchy. In 1984 Furst, Saxe, and Sipser showed that calculating the PARITY of the input bits (unlike the aforementioned addition/subtraction problems
AC0
Fractal composed of triangles
to another, form an undirected graph, the Hanoi graph, that can be represented geometrically as the intersection graph of the set of triangles remaining
Sierpiński_triangle
1979 classic textbook on computational complexity theory
homeomorphism (for a fixed graph H) Graph genus Chordal graph completion Chromatic index Spanning tree parity problem Partial order dimension Precedence constrained
Computers_and_Intractability
Region of Japan
economy, with the largest gross metropolitan product at purchasing power parity (PPP) in the world according to a study by PricewaterhouseCoopers. Sources:
Kantō_region
Model of computational complexity
Boolean circuit with n {\displaystyle n} input bits is a directed acyclic graph in which every node (usually called gates in this context) is either an
Circuit_complexity
Economic theory
flexible, that arbitrage in asset markets holds, via the uncovered interest parity equation, and that expectations of exchange rate changes are "consistent":
Overshooting_model
European system to reduce exchange rate variability after the Euro
Irish pound's parity with sterling in 1979, because the UK had decided not to participate. (The Irish Central Bank had maintained parity with sterling
European Exchange Rate Mechanism
European_Exchange_Rate_Mechanism
American mathematician
Her research involves coding theory, including low-density parity-check codes and Tanner graphs. After "a rough start" in a required calculus course as an
Christine_Kelley
Model of the atomic nucleus
states of even (positive) parity. Similarly, every odd level includes only states of odd (negative) parity. Thus we can ignore parity in counting states. The
Nuclear_shell_model
Guidance and navigation computer used in Apollo spacecraft
IC packages. The AGC has a 16-bit word length, with 15 data bits and one parity bit. Most of the software on the AGC is stored in a special read-only memory
Apollo_Guidance_Computer
True when either but not both inputs are true
odd number of the variables are true), which is equal to the parity bit returned by a parity function. In logical circuits, a simple adder can be made with
Exclusive_or
Spreadsheet editor by Microsoft
iOS and iPadOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic
Microsoft_Excel
Complexity class
zero? (subset sum problem) Are there any Hamiltonian cycles in a given graph with cost less than 100? (traveling salesman problem) Are there any variable
♯P
permutation Derangement Even and odd permutations—see Parity of a permutation Josephus permutation Parity of a permutation Separable permutation Stirling permutation
List_of_permutation_topics
Measure of an economy's energy inefficiency
economies The graph shows the amount of energy it takes to produce a US $ of GNP for selected countries. GNP is based on 2004 purchasing power parity and 2000
Energy_intensity
Game of chance and hand game
coins instead of fingers. Parity game – an unrelated (and much more complicated) two-player logic game, played on a colored graph. Rock paper scissors –
Odds_and_evens_(hand_game)
rates with other major currencies, in both nominal and purchasing power parity (PPP) terms. After taking power in 1978, Deng Xiaoping started the reform
List of renminbi exchange rates
List_of_renminbi_exchange_rates
Type of error-correcting code using convolution
a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to
Convolutional_code
Acceptance by a nondeterministic parity automaton of the empty tree corresponds to a parity game on a finite graph G. Using the above positional (also
S2S_(mathematics)
Rechargable battery used for vehicles
debated. This can delay cost parity. The mass of the electric vehicle battery is the limiting factor to reach range parity. Diesel and gasoline have more
Electric_vehicle_battery
8-bit microprocessor
portable devices, including the Game Gear and the TI-81 and succeeding graphing calculators. The Z80 was the brainchild of Federico Faggin, a key figure
Zilog_Z80
Machine learning method to transfer knowledge from a large model to a smaller one
and natural language processing. Recently, it has also been introduced to graph neural networks applicable to non-grid data. Knowledge transfer from a large
Knowledge_distillation
Period of the Fibonacci sequence modulo an integer
Theorem of the Day (2015). Retrieved 7 January 2016. Freyd & Brown (1992) Graph of the cycles modulo 1 to 24. Each row of the image represents a different
Pisano_period
drawn criticism for their payroll, with some claiming it undermines the parity of MLB. From 2003 to 2024, the Yankees' payroll exceeded the luxury tax
List of highest-paid Major League Baseball players
List_of_highest-paid_Major_League_Baseball_players
Graph drawn with all edges intersecting
A thrackle is an embedding of a graph in the plane in which each edge is a Jordan arc and every pair of edges meet exactly once. Edges may either meet
Thrackle
Result about flat-foldable origami crease patterns
even number. This implies (via a form of planar graph duality between Eulerian graphs and bipartite graphs) that, for any flat-foldable crease pattern, it
Maekawa's_theorem
Series of graphing calculators
The HP 48 is a series of graphing calculators designed and produced by Hewlett-Packard from 1990 until 2003. The series includes the HP 48S, HP 48SX, HP 48G
HP_48_series
PARITY GRAPH
PARITY GRAPH
Girl/Female
Muslim
Purity, Refinement, Clarity
Female
English
Pet form of English Cara, CARITA means "beloved" or "friend."
Girl/Female
Muslim
Clarity, Purity, Serenity
Girl/Female
Muslim
Purity, Clarity, Serenity
Female
Persian/Iranian
(پریسا) Persian name PARISA means either "angelic" or "like a fairy."
Girl/Female
Indian
Beautiful
Girl/Female
British, English
Purity
Girl/Female
Arabic, Muslim
Purity; Refinement; Clarity
Girl/Female
Hindu
Like Paris, Fairy or like a fairy
Girl/Female
Hindu, Indian, Marathi
Angel; In Each Detection
Girl/Female
American, Australian, British, Christian, English, German, Indian, Latin
Act of Kindness; Charity; Brotherly Love; Affection
Girl/Female
Indian
Clarity, Purity, Serenity
Boy/Male
Hindu, Indian
Affection; Love
Girl/Female
Hindu
In each direction
Female
English
 English name derived from the vocabulary word charity, from Latin caritas, from carus, CHARITY means "dear." It is one of the virtue names that were popular with the Puritans; some others are Chastity, Faith, Honor, Hope, and Prudence.Â
Girl/Female
Indian
Purity, Clarity, Serenity
Female
Spanish
 Pet form of Spanish MarÃa, MARITA means "obstinacy, rebelliousness" or "their rebellion."
Female
English
English name derived from the vocabulary word clarity, from Latin clarus, CLARITY means "clear."
Female
Norwegian
 Norwegian name derived from Latin caritas, from carus, KARITA means "dear."Â
Male
Italian
Italian form of Greek Paris, probably PARIDE means "wager."Â
PARITY GRAPH
PARITY GRAPH
Boy/Male
Hindu, Indian
Winning of Hearts
Boy/Male
Indian
Happy, Advances
Girl/Female
Bengali, Indian, Telugu
Goddess of Health
Boy/Male
Indian, Tamil
Loving
Boy/Male
Tamil
Parnabha | பரà¯à®¨à®¾à®ªà®¾Â
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Clever; Skilled
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English, Indian, Jamaican
From the Old Town; Ella's Town
Boy/Male
Arabic
Militant; Warlike; Heroic
Girl/Female
Tamil
Dayamayee | தயாமயீ
Kind, Merciful
Boy/Male
Welsh Celtic
Incredibly strong.
PARITY GRAPH
PARITY GRAPH
PARITY GRAPH
PARITY GRAPH
PARITY GRAPH
v.
A part or portion.
v. t.
To write a parody upon; to burlesque.
n.
The quality or condition of being equal or equivalent; A like state or degree; equality; close correspondence; analogy; as, parity of reasoning.
v.
A number of persons invited to a social entertainment; a select company; as, a dinner party; also, the entertainment itself; as, to give a party.
v. t.
To make pure or clear from material defilement, admixture, or imperfection; to free from extraneous or noxious matter; as, to purify liquors or metals; to purify the blood; to purify the air.
v.
One concerned or interested in an affair; one who takes part with others; a participator; as, he was a party to the plot; a party to the contract.
v.
A part of a larger body of company; a detachment; especially (Mil.), a small body of troops dispatched on special service.
n.
A hollow place; a hollow; as, the abdominal cavity.
a.
Of or pertaining to a parish; parochial; as, a parish church; parish records; a parish priest; maintained by the parish; as, parish poor.
v.
Partial; favoring one party.
n.
Freedom from guilt or the defilement of sin; innocence; chastity; as, purity of heart or of life.
n.
Indivisibility into equal parts; oddness.
v.
Parted or divided, as in the direction or form of one of the ordinaries; as, an escutcheon party per pale.
v. t.
To free from improprieties or barbarisms; as, to purify a language.
n.
The quality or state of being rare; rareness; thinness; as, the rarity (contrasted with the density) of gases.
v.
A person; as, he is a queer party.
n.
Freedom from foreign idioms, or from barbarous or improper words or phrases; as, purity of style.
adv.
Partly.
n.
freedom from foreign admixture or deleterious matter; as, the purity of water, of wine, of drugs, of metals.
n.
Smallnes of quantity; exiguity; insufficiency; as, paucity of blood.