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Graph which is isomorphic to its complement
of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are
Self-complementary_graph
Graph with same nodes as but complementary connections to another
characterization of self-complementary graphs. Several classes of graphs are self-complementary, in the sense that the complement of any graph in one of these
Complement_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
graph is self-complementary, and is also a circulant graph. More generally every Paley graph of prime order is a self-complementary circulant graph.
Circulant_graph
self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex-connected graph and a 1-edge-connected graph
Bull_graph
Graph of numbers differing by a square
x ± 3 (mod 13), and x ± 4 (mod 13). The Paley graphs are self-complementary: the complement of any Paley graph is isomorphic to it. One isomorphism is via
Paley_graph
Unsolved problem in computational complexity theory
bipartite Eulerian graphs bipartite regular graphs line graphs split graphs chordal graphs regular self-complementary graphs polytopal graphs of general, simple
Graph_isomorphism_problem
Topics referred to by the same term
complement Ones' complement Two's complement Complement graph Self-complementary graph, a graph which is isomorphic to its complement Complemented lattice
Complement
Topics referred to by the same term
physics Antisymmetric relation in mathematics Skew-symmetric graph Self-complementary graph In mathematics, especially linear algebra, and in theoretical
Antisymmetric
Topics referred to by the same term
chains in immunoglobulins Complementary angles, in geometry Self-complementary graph, in graph theory Yin and yang, complementary relation between apparent
Complementarity
Infinite graph containing all countable graphs
Rado graph. Therefore, the Rado graph is a self-complementary graph. In one of Ackermann's original 1937 constructions, the vertices of the Rado graph are
Rado_graph
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Graph in graph theory
C(H). In particular, the lexicographic product of two self-complementary graphs is self-complementary. The independence number of a lexicographic product
Lexicographic product of graphs
Lexicographic_product_of_graphs
Concept in graph theory
Paley graph of order q is an srg(q, (q − 1)/2, (q − 5)/4, (q − 1)/4). The smallest Paley graph, with q = 5, is the 5-cycle (above). Self-complementary arc-transitive
Strongly_regular_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Graph linking pairs of comparable elements in a partial order
cocomparability graphs is self-complementary in the sense that the complement of a cocomparability graph is a comparability graph, and vice versa. Interval graphs are
Comparability_graph
Special case of a strongly regular graph
conference graph is always a conference graph with the same parameters, and in many cases is self-complementary, such as for all the Paley graphs. Brouwer
Conference_graph
Array of nonnegative integers in combinatorics
symmetric self-complementary if it is cyclically symmetric and self-complementary. The figure presents a cyclically symmetric self-complementary plane partition
Plane_partition
Perfect graphs have neither odd holes nor odd antiholes
Berge's forbidden graph characterization is self-complementary, the weak perfect graph theorem follows immediately from the strong perfect graph theorem. The
Strong_perfect_graph_theorem
Graph formed by adding isolated or universal vertices
This also explains why threshold graphs are closed under taking complements; the P4 is self-complementary, hence if a graph is P4-, C4- and 2K2-free, its
Threshold_graph
Czech mathematician (1933–2018)
Chvatal, V.; Erdös, P.; Hedrlín, Z. (1972). "Ramsey's theorem and self-complementary graphs". Discrete Mathematics. 3 (4): 301–304. doi:10.1016/0012-365X(72)90087-8
Zdeněk_Hedrlín
Problem in graph theory
edges between S and the complementary subset is as large as possible. Equivalently, one wants a bipartite subgraph of the graph with as many edges as possible
Maximum_cut
Probability of survival beyond any specified time
The survival function is the complementary cumulative distribution function of the lifetime. Sometimes complementary cumulative distribution functions
Survival_function
Undirected bipartite graph with 112 vertices and 168 edges
The Ljubljana graph was first published in 1993 by Brouwer, Dejter and Thomassen as a self-complementary subgraph of the Dejter graph. In 1972, Bouwer
Ljubljana_graph
Directed graph isomorphic to its own transpose graph
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by
Skew-symmetric_graph
Process of forming order by local interactions
random graphs, and some instances of evolutionary computation and artificial life exhibit features of self-organization. In swarm robotics, self-organization
Self-organization
Matroid with complemented basis sets
their bases, is self-complementary, so the dual of a matroid is necessarily a matroid. The flats of M {\displaystyle M} are complementary to the cyclic
Dual_matroid
Two pentagonal pyramids fused base-to-base
give rise to a graph. It is one of the four four-connected simplicial well-covered graphs. It is also one of the six connected graphs in which its neighborhood
Pentagonal_bipyramid
Points and lines with equal incidences
doi:10.1515/advgeom-2015-0019. Coxeter, H.S.M. (1999), "Self-dual configurations and regular graphs", The Beauty of Geometry, Dover, ISBN 0-486-40919-8 Dembowski
Configuration_(geometry)
Process forming a path from many random steps
simple path Maximal entropy random walk – Type of biased random walk on a graph Self-avoiding walk – Sequence of moves on a lattice Unit root – Feature of
Random_walk
Geometric system of two mutually inscribed tetrahedra
German), 27 (2): 359–366. Coxeter, H. S. M. (1950), "Self-dual configurations and regular graphs", Bulletin of the American Mathematical Society, 56 (5):
Möbius_configuration
Problem-solving method
first printing in 1945-copies sold number in the hundreds of thousands. Complementary to How To Solve It are two other works, each in two volumes: Mathematical
Heuristic
7-cube girth 4. It seems that the Dejter graph is the smallest symmetric graph having a connected self-complementary vertex-spanning semi-symmetric cubic
Dejter_graph
Operation in graph theory
If a graph is locally equivalent to its complement, it is self-complementary. The number of essentially different ways of transforming one graph into
Local_complementation
General concept and operation in mathematics
polyhedron, one can form a planar graph, the graph of its vertices and edges. The dual polyhedron has a dual graph, a graph with one vertex for each face
Duality_(mathematics)
Solid with twenty equal triangular faces
is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra and other
Regular_icosahedron
Sensory system that receives and integrates information from the body
PMID 27172277. Kessler, RC; Soukup, J; Davis, RB; et al. (2001). "The Use of Complementary and Alternative Therapies to Treat Anxiety and Depression in the United
Interoception
mathematics, a contraharmonic mean (or antiharmonic mean) is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the
Contraharmonic_mean
search engine in 1990, and subsequent developments in the field. It is complementary to the history of web search engines page that provides more qualitative
Timeline of web search engines
Timeline_of_web_search_engines
Scale for measuring sexual orientation
Kinsey, Wardell Pomeroy, and others, and were also prominent in the complementary work Sexual Behavior in the Human Female (1953). Alfred Kinsey, the
Kinsey_scale
Settlement without third party involvement
Merseyside ). Many other monetary innovations—including local currency and complementary currency systems—fall under the category of collaborative finance. For
Collaborative_finance
Independence system partitionable into circuits
generalization of the Eulerian graphs, graphs in which every vertex has even degree. By Veblen's theorem the edges of every such graph may be partitioned into
Eulerian_matroid
Process of generalization
they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see
Abstraction
Subset of artificial intelligence
methods are based on estimated density and graph connectivity. A special type of unsupervised learning called self-supervised learning involves training a
Machine_learning
Device performing a Boolean function
PMOS and NMOS gates. Both types were later combined and adapted into complementary MOS (CMOS) logic by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor
Logic_gate
Analysing a string of symbols, according to the rules of a formal grammar
visual languages are sometimes based on graph grammars. Adaptive parsing algorithms have been used to construct "self-extending" natural language user interfaces
Parsing
System with multiple networked computers
different kinds of network graphs, such as undirected rings, unidirectional rings, complete graphs, grids, directed Euler graphs, and others. A general method
Distributed_computing
Economic model for sustainable development (created 2012)
or lifebelt – combining the concept of planetary boundaries with the complementary concept of social boundaries. The name derives from the shape of the
Doughnut_(economic_model)
Form of second-order logic
with no edges connecting them to the rest of the graph. The complementary problem, testing whether a graph is connected, does not belong to monadic NP. That
Monadic_second-order_logic
1007/s00454-005-1224-9, MR 2202110. Coxeter, H. S. M. (1950), "Self-dual configurations and regular graphs", Bulletin of the American Mathematical Society, 56:
Cremona–Richmond configuration
Cremona–Richmond_configuration
Mathematical model of ferromagnetism in statistical mechanics
vertex set V(G) of a weighted undirected graph G determines a cut of the graph G into S and its complementary subset G\S. The size of the cut is the sum
Ising_model
A complex representation is self-conjugate if it is isomorphic to its complex conjugate. complementary A complementary representation to a subrepresentation
Glossary of representation theory
Glossary_of_representation_theory
Research integrity risk metric
Librarian at the American University of Beirut, RI² is presented as complementary to conventional global university rankings, which primarily emphasize
Research_Integrity_Risk_Index
Machine learning methods using multiple input modalities
two-dimensional pixel image, for instance by converting a method's control-flow graph into a black-and-white image processed with a convolutional neural network
Multimodal_learning
Canadian mathematician
in a graph". Discrete Mathematics. 185 (1–3): 245–248. doi:10.1016/S0012-365X(97)00213-6. Dominique De Caen (1998). "The Spectra of Complementary Subgraphs
Dominique_de_Caen
Conscious subjective experience
sometimes conceptualize emotion in different ways and at other times in complementary ways. Many of these different approaches were synthesized by Turner
Emotion
Origins and events of data
data flow reconstruction is computing an association graph from the lineage information. The graph represents the steps in the data flow. The actors act
Data_lineage
Free online crowdsourced encyclopedia
Wikipedia's launch, but with limited success. Wikipedia began as a complementary project for Nupedia, a free online English-language encyclopedia project
Wikipedia
Study of the attraction between people that leads to friendship or romance
self than to those who did not. Specifically, low self-esteem individuals appeared more likely to desire a complementary relationship than high self-esteem
Interpersonal_attraction
Ionic structure in solution
tailored properties. Graph Theory Analysis: Ions often self-assemble into large and polydisperse aggregates in solution. Graph-theoretical approaches
Ion_network
Idempotent linear transformation from a vector space to itself
\in U,\mathbf {v} \in V.} The image and kernel of a projection are complementary, as are P {\displaystyle P} and Q = I − P {\displaystyle Q=I-P} . The
Projection_(linear_algebra)
Model in development economics
the help of the graph on the right, which is an integration of the industrial sector graph with an inverted agricultural sector graph, such that the origin
Fei–Ranis model of economic growth
Fei–Ranis_model_of_economic_growth
Cryptocurrency
(Abbreviation: XNO) is a cryptocurrency characterized by a directed acyclic graph data structure and distributed ledger, making it possible for Nano to work
Nano_(cryptocurrency)
System of elements that are subordinated to each other
authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form. Hierarchies have their own
Hierarchy
Hypothetical faster-than-light particle
term tachyon comes from the Greek: ταχύς, tachus, meaning swift. The complementary particle types are called luxons (which always move at the speed of
Tachyon
Property of a thermodynamic system
amount λ {\textstyle \lambda } in the state X 1 {\textstyle X_{1}} and a complementary amount, ( 1 − λ ) {\textstyle (1-\lambda )} , in the state X 0 {\textstyle
Entropy
Large-scale brain network active when not focusing on an external task
suggests that each DMN node can be decomposed into subregions with complementary structural and functional properties. It has been a widespread practice
Default_mode_network
Type of vector space in math
to the closed graph theorem, which asserts that a linear function from one Banach space to another is continuous if and only if its graph is a closed set
Hilbert_space
Numbers obtained by adding the two previous ones
the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed
Fibonacci_sequence
Threshold of percolation theory models
1590/S0103-97332003000300025. S2CID 8972025. Lee, M. J. (2007). "Complementary algorithms for graphs and percolation". Physical Review E. 76 (2) 027702. arXiv:0708
Percolation_threshold
Convex polyhedron with 12 triangular faces
intersect, and when they cross an edge of the polyhedron, they make complementary angles on the two incident faces to the edge. Intuitively, one could
Snub_disphenoid
Theory on how and why new ideas spread
inter-city innovation networks in China using temporal exponential random graph models (TERGM), highlighting the role of network evolution in shaping innovation
Diffusion_of_innovations
Technique in analytical chemistry
detector such as UV detectors, which produces a graph (the chromatogram). A chromatogram is a graph of detector signal intensity versus time or the volume
High-performance liquid chromatography
High-performance_liquid_chromatography
Pollution around Earth by defunct artificial objects
2010 Beijing Orbital Debris Mitigation Workshop, 18–19 October 2010, see graph p. 4. Archived 9 March 2012 at the Wayback Machine. Gebrekidan, Selam (31
Space_debris
Generalized notion of counting curve intersections
formula states: let X be a regular variety, V and W two subvarieties of complementary dimension such that V ∩ W is zero-dimensional. For any point x ∈ V ∩
Intersection_number
Particle physics process
di-Higgs production (HH), is a process in particle physics regarding the self-interactions of the Higgs boson. This process is essential for testing the
Higgs_pair_production
Infinite integer series where the next number is the sum of the two preceding it
are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences. The Lucas sequence has the same recursive
Lucas_number
entire range. Complementary distribution functions for the exponential and Pareto distributions are shown below. Shown on the left is a graph of the distributions
Long-tail_traffic
Mathematical function common in physics
function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the
Stretched exponential function
Stretched_exponential_function
2003 American teen drama television series
soon discovers that he deals with similar issues to his new peers, such as self-identity conflict and familial alienation. The relationship between Ryan
The_O.C.
Competitive algorithm for searching a problem space
case. Tree-like representations are explored in genetic programming and graph-form representations are explored in evolutionary programming; a mix of
Genetic_algorithm
Interviewing method based on personal construct theory of personality
practitioners to use semantic network techniques in addition to the repertory grid. Graph (abstract data type) Implicit Relational Assessment Procedure Knowledge
Repertory_grid
Logical principle
vagueness Limited principle of omniscience – Mathematical concept Logical graph – Type of diagrammatic notation for propositional logicPages displaying
Law_of_excluded_middle
System that regulates the formation of blocks on a blockchain
Retrieved 2007-11-04. Tromp, John (2015). "Cuckoo Cycle: A Memory Bound Graph-Theoretic Proof-of-Work" (PDF). Financial Cryptography and Data Security
Proof_of_work
AMD computing architecture
describe the AI engine instantiation, placement and connection is named AIE graph. The official programming model suggested by AMD requires writing such a
AI_engine
statics – Compensating differential – Competition – Competition law – Complementary good – Complexity economics – Comprehensive Income Policy Agreement
Index_of_economics_articles
Analysis of variance Analytic and enumerative statistical studies Ancestral graph Anchor test Ancillary statistic ANCOVA – redirects to Analysis of covariance
List_of_statistics_articles
Generation of text in natural languages
programming languages, which makes NLG more challenging. NLG may be viewed as complementary to natural language understanding (NLU): whereas in natural-language
Natural_language_generation
Equations of light transmission and reflection
to be s or p polarized, an artifact of the adopted sign convention (see graph for an air-glass interface at 0° incidence). The equations consider a plane
Fresnel_equations
Algorithms for solving convex optimization problems
the "perturbed complementarity" condition, for its resemblance to "complementary slackness" in KKT conditions. We try to find those ( x μ , λ μ ) {\displaystyle
Interior-point_method
Probability distribution
masks the underlying simplicity of the function when plotted on a log-log graph, which then takes the form of a straight line with negative gradient: It
Pareto_distribution
Hypothesis that human replicas elicit revulsion
once again and approaches human-to-human empathy levels. When plotted on a graph, the reactions are indicated by a steep decrease followed by a steep increase
Uncanny_valley
Retrieved 22 September 2019. Shen, Weixiao (2018). "Hausdorff dimension of the graphs of the classical Weierstrass functions". Mathematische Zeitschrift. 289
List of fractals by Hausdorff dimension
List_of_fractals_by_Hausdorff_dimension
Chinese view of heaven
needed] In Taoism and Confucianism, Tian is described in relation to its complementary aspect Dì (地), which is the term for Earth. Together, they were understood
Tian
Field dedicated to organizing and structuring biomedical data
knowledge into structured formats, such as spreadsheets, tables and knowledge graphs. The biocuration of biomedical knowledge is made possible by the cooperative
Biocuration
Unequal access to higher quality healthcare
equally between out-of-pocket funding and private insurance, which may be complementary (meeting costs not covered by the public system such as the cost of
Two-tier_healthcare
Opinion and argument mining subtask
language models have also been explored as a means of leveraging the complementary strengths of discriminative and generative approaches, with voting-based
Stance_detection
Functional gastrointestinal disorder
(August 2022). "Heart Rate Variability-An Index of the Efficacy of Complementary Therapies in Irritable Bowel Syndrome: A Systematic Review". Nutrients
Irritable_bowel_syndrome
Study of the inheritance of continuously variable traits
of inbreeding of all types, as can be seen in the graphs above. The selfing curve is, in fact, a graph of the coefficient of parentage. These are derived
Quantitative_genetics
Type of imaging sensor
reconstruction can be achieved using temporal smoothing, e.g. high-pass or complementary filter. Alternative methods include optimization and gradient estimation
Event_camera
travel, tourism, insurance
SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
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SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
SELF COMPLEMENTARY-GRAPH
travel, tourism, insurance