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Undirected graph with no non-trivial symmetries
In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism
Asymmetric_graph
Area of discrete mathematics
undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the
Graph_theory
Graph in which all ordered pairs of linked nodes are automorphic
conventionally the term "symmetric graph" is not complementary to the term "asymmetric graph," as the latter refers to a graph that has no nontrivial symmetries
Symmetric_graph
Assignment of colors to graph vertices that destroys all symmetries
and only if it is asymmetric. For instance, the Frucht graph has a distinguishing coloring with only one color. In a complete graph, the only distinguishing
Distinguishing_coloring
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Mapping a graph onto itself without changing edge-vertex connectivity
automorphisms: An asymmetric graph is an undirected graph with only the trivial automorphism. A vertex-transitive graph is an undirected graph in which every
Graph_automorphism
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
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
Graph of numbers differing by a square
Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic
Paley_graph
NP-hard problem in combinatorial optimization
yield a TSP problem in asymmetric form. An equivalent formulation in terms of graph theory is: Given a complete weighted graph (where the vertices would
Travelling_salesman_problem
Square matrix used to represent a graph or network
The adjacency matrix of a directed graph can be asymmetric. One can define the adjacency matrix of a directed graph either such that a non-zero element
Adjacency_matrix
Absence of, or a violation of, symmetry
Examples include asymmetric relations, asymmetry of shapes in geometry, asymmetric graphs et cetera. In geometry, a figure is asymmetric if it does not
Asymmetry
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
Graph where each vertex has the same number of neighbors
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular
Regular_graph
Cubic graph with 12 vertices and 18 edges
distinguished topologically from every other vertex. Such graphs are called asymmetric (or identity) graphs. Frucht's theorem states that any finite group can
Frucht_graph
unlabelled graphs with n {\displaystyle n} vertices is still not known in a closed-form solution, but as almost all graphs are asymmetric this number
Graph_enumeration
Branch of mathematics
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatorial
Algebraic_graph_theory
Length of shortest path between two nodes of a graph
mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting
Distance_(graph_theory)
Directed graph where each vertex pair has one arc
Equivalently, a tournament is a complete asymmetric relation. The name tournament comes from interpreting the graph as the outcome of a round-robin tournament
Tournament_(graph_theory)
Dimensionality reduction of graph-based semantic data objects [machine learning task]
product, it can distinguish symmetric and asymmetric facts. This approach is scalable to a large knowledge graph in terms of time and space cost. ANALOGY:
Knowledge_graph_embedding
Graph where all pairs of vertices are automorphic
regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such
Vertex-transitive_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
On chains and antichains in partial orders
comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements. An undirected graph is perfect
Dilworth's_theorem
Graph linking pairs of comparable elements in a partial order
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability
Comparability_graph
Graph property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices
Distance-regular_graph
Australian philosopher (born 1963)
special issue on the theme 'Ethics and Religion'.) 'The World is not an Asymmetric Graph', Analysis 71 (2011): 3–10. 'The Metaphysical Foundations of Natural
David_S._Oderberg
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Smallest transitive relation containing a given binary relation
closure and transitive reduction are also used in the closely related area of graph theory. A relation R on a set X is transitive if, for all x, y, z in X,
Transitive_closure
Binary relation over a set and itself
endorelations. Terminology particular for graph theory is used for description, with an ordinary (undirected) graph presumed to correspond to a symmetric
Homogeneous_relation
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Any diagram where a curve originally falls, then steeply rises
The asymmetric J-curve implies that there could be an asymmetric relationship between the exchange rate changes and trade balance. The asymmetric effects
J_curve
Graph where any two nodes of equal distance are isomorphic
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any
Distance-transitive_graph
Graph where all pairs of edges are automorphic
In the mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism
Edge-transitive_graph
Visual depiction of a partially ordered set
automatically using graph drawing techniques. In some sources, the phrase "Hasse diagram" has a different meaning: the directed acyclic graph obtained from
Hasse_diagram
Logical formulation of graph properties
the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences
Logic_of_graphs
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Mathematical tree with cycle through leaves
two embedded Halin graphs as the same when they are mirror reflections of each other. When reflections of asymmetric Halin graphs are counted as distinct
Halin_graph
Graph that is edge-transitive and regular but not vertex-transitive
graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is
Semi-symmetric_graph
Relationship between two sets, defined by a set of ordered pairs
if xRx holds for no x. It is symmetric if xRy always implies yRx, and asymmetric if xRy implies that yRx is impossible. It is transitive if xRy and yRz
Relation_(mathematics)
In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph G = ( U , V , E ) {\displaystyle G=(U,V,E)} for which
Biregular_graph
Type of graph in graph theory
of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is
Half-transitive_graph
Human-face shaped display of data
visual parsing. Chernoff faces themselves can be plotted on a standard X–Y graph; the faces can be positioned X–Y based on the two most important variables
Chernoff_face
Type of graph in graph theory
mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing
Hypohamiltonian_graph
Reflexive and transitive binary relation
relations, preorders (on a nonempty set) are never asymmetric. A preorder can be visualized as a directed graph, with elements of the set corresponding to vertices
Preorder
2018 asymmetric board game
Root: A Game of Woodland Might and Right is a 2018 asymmetric strategy wargame board game designed by Cole Wehrle, illustrated by Kyle Ferrin, and published
Root_(board_game)
different domains can be presented as DCOPs. The graph coloring problem is as follows: given a graph G = ⟨ N , E ⟩ {\displaystyle G=\langle N,E\rangle
Distributed constraint optimization
Distributed_constraint_optimization
Bipartite graph partition with special property
different decomposition of a bipartite graph, which is asymmetric - it distinguishes between vertices in one side of the graph and the vertices on the other side
Dulmage–Mendelsohn decomposition
Dulmage–Mendelsohn_decomposition
On graphs with given symmetry groups
subgraph is itself asymmetric and two replacements are isomorphic if and only if they replace edges of the same color, then the undirected graph created by performing
Frucht's_theorem
In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for
Zero-symmetric_graph
group Fn is a topological space consisting of the so-called "marked metric graph structures" of volume 1 on Fn. The Outer space, denoted Xn or CVn, comes
Outer_space_(mathematics)
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Relationship between elements of two sets
relations leans on graph theory: For relations on a set (homogeneous relations), a directed graph illustrates a relation and a graph a symmetric relation
Binary_relation
Measure of similarity and diversity between sets
In practice, graph representations like adjacency lists are used to improve the efficiency of intersection and union math. For large graphs, computing similarity
Jaccard_index
Functions such that f(–x) equals f(x) or –f(x)
are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect
Even_and_odd_functions
Search algorithm
Monte-Carlo method to bias search into the largest Voronoi regions of a graph in a configuration space. Some variations can even be considered stochastic
Rapidly_exploring_random_tree
Characterizes the height of any finite partially ordered set
complement graph of a comparability graph is perfect. The perfect graph theorem of Lovász (1972) states that the complements of perfect graphs are always
Mirsky's_theorem
Proving validity without revealing other data
large graph G. Victor knows G but not the cycle (e.g., Peggy has generated G and revealed it to him.) Finding a Hamiltonian cycle given a large graph is
Zero-knowledge_proof
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
Symmetry breaking through the vacuum state
which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion
Spontaneous_symmetry_breaking
Property of a relation on a set
{\overline {R}}\subseteq R^{\top }} ; R ¯ {\displaystyle {\overline {R}}} is asymmetric, where U {\displaystyle U} is the universal relation and R ⊤ {\displaystyle
Connected_relation
Mathematical models of strategic interactions
non-cooperative games. Formally, using graph theory, a vNM set can be defined as follows. Let D denote a simple directed graph, D = ( X , Δ ) {\displaystyle D=(X
Game_theory
Polyhedron formed by joining mirroring pyramids base-to-base
distance from the base. The dual of an asymmetric right n-gonal bipyramid is an n-gonal frustum. A regular asymmetric right n-gonal bipyramid has symmetry
Bipyramid
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
relationship in directed trees and directed series–parallel graphs. The comparability graphs of series-parallel partial orders are cographs. Series-parallel
Series-parallel_partial_order
Complexity class
from an asymmetric General-Congestion-Game/Change to symmetric General-Congestion-Game/Change. Finding a pure Nash Equilibrium in an Asymmetric
PLS_(complexity)
Mathematical set with an ordering
homogeneous relation < on a set P {\displaystyle P} that is irreflexive, asymmetric and transitive; that is, it satisfies the following conditions for all
Partially_ordered_set
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
Partition of vertices of a directed graph
In graph theory, the weak components of a directed graph partition the vertices of the graph into subsets that are totally ordered by reachability. They
Weak_component
Shape made from cubes joined together
similarly-named notions of a dual polyhedron, and of the dual graph of a surface-embedded graph. Dual graphs have also been used to define and study special subclasses
Polycube
Order-preserving mathematical function
The graph of a monotone operator G ( T ) {\displaystyle G(T)} is a monotone set. A monotone operator is said to be maximal monotone if its graph is a
Monotonic_function
Generalized alphabetical order
extension theorem Zorn's lemma Properties & Types (list) Antisymmetric Asymmetric Boolean algebra topics Completeness Connected Covering Dense Directed
Lexicographic_order
American singer-songwriter (born 1989)
synthesizers, and drum pads. Evermore experiments with varied song structures, asymmetric time signatures, and diverse instruments. Critics deemed the indie styles
Taylor_Swift
in an undirected graph. Until this time, it could be placed only in NL, despite seeming not to require nondeterminism (the asymmetric variant STCON was
Symmetric_Turing_machine
System that regulates the formation of blocks on a blockchain
profit from shorting Bitcoin or for non-economic reasons. Bitcoin has asymmetric security where Bitcoin miners control its security, but they aren't the
Proof_of_work
Scientific theory in vertebrate development
frontal lobes are asymmetric to the left (the right lobe appears slightly larger than the left), whereas the occipital lobe is asymmetric to the right; the
Axial_twist_theory
In mathematics, with negligible exceptions
commonly used for this concept. Example: Almost all graphs are asymmetric. Almost all graphs have diameter 2. In topology and especially dynamical systems
Almost_all
Subset of incomparable elements
"The complexity of counting cuts and of computing the probability that a graph is connected", SIAM Journal on Computing, 12 (4): 777–788, doi:10.1137/0212053
Antichain
Probability theorem on no events occurring
A statement of the asymmetric version (which allows for events with different probability bounds) is as follows: Lemma (asymmetric version). Let A = {
Lovász_local_lemma
Group of transformations under which the object is invariant
containing only the identity operation, which occurs when the figure is asymmetric, for example the letter "F". C2 is the symmetry group of the letter "Z"
Symmetry_group
Method of bypassing authentication or encryption in a computer
deep generative models, reinforcement learning (e.g., AI GO), and deep graph models. These broad-ranging potential risks have prompted concerns from
Backdoor_(computing)
Algebraic object with an ordered structure
extension theorem Zorn's lemma Properties & Types (list) Antisymmetric Asymmetric Boolean algebra topics Completeness Connected Covering Dense Directed
Ordered_field
Property of elements related by inequalities
Hoffman, A. J. (1964), "A characterization of comparability graphs and of interval graphs", Canadian Journal of Mathematics, 16: 539–548, doi:10.4153/CJM-1964-055-5
Comparability
Mathematical ranking of a set
(PDF) on 2018-04-06, Lemma 1.1 (iv). Note that this source refers to asymmetric relations as "strictly antisymmetric". Such a relation is also called
Weak_ordering
Type of graph used in research
A funnel plot is a graph designed to check for the existence of publication bias; funnel plots are commonly used in systematic reviews and meta-analyses
Funnel_plot
extension theorem Zorn's lemma Properties & Types (list) Antisymmetric Asymmetric Boolean algebra topics Completeness Connected Covering Dense Directed
Absolutely and completely monotonic functions and sequences
Absolutely_and_completely_monotonic_functions_and_sequences
pyramid, with less than 250,000 males and females between 0–10 years old. The graph only gets narrower as it goes up with virtually no-one living past 50 years
Demographics_of_Rwanda
Partially ordered topological space
closed partial order ≤ {\displaystyle \leq } , i.e. a partial order whose graph { ( x , y ) ∈ X 2 ∣ x ≤ y } {\displaystyle \{(x,y)\in X^{2}\mid x\leq y\}}
Partially_ordered_space
real number line Antichain Strict order Hasse diagram Directed acyclic graph Duality (order theory) Product order Greatest element (maximum, top, unit)
List_of_order_theory_topics
Size of subsets in order theory
extension theorem Zorn's lemma Properties & Types (list) Antisymmetric Asymmetric Boolean algebra topics Completeness Connected Covering Dense Directed
Cofinality
Measure of centrality in a network based on nodal influence
In graph theory, the Katz centrality or alpha centrality of a node is a measure of centrality in a network. It was introduced by Leo Katz in 1953 and
Katz_centrality
Reversal of the order of elements of a binary relation
inclusion. If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, connected, trichotomous, a partial order, total order, strict
Converse_relation
Asymmetric sigmoid function
^{-ct}}=a\mathrm {e} ^{0}=a} b sets the displacement along the x-axis (translates the graph to the left or right). c sets the growth rate (y scaling) e is Euler's Number
Gompertz_function
Coordinates comprising a distance and an angle
well as systems with point sources, such as radio antennas. Radially asymmetric systems may also be modeled with polar coordinates. For example, a microphone's
Polar_coordinate_system
Well-quasi-ordering of finite trees
transfinite recursion). In 2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important
Kruskal's_tree_theorem
extension theorem Zorn's lemma Properties & Types (list) Antisymmetric Asymmetric Boolean algebra topics Completeness Connected Covering Dense Directed
Reflexive_closure
Mathematical function having a characteristic S-shaped curve or sigmoid curve
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is
Sigmoid_function
Alternative mathematical ordering
picture. A ternary relation is called a cyclic order if it is cyclic, asymmetric, transitive, and connected. Dropping the "connected" requirement results
Cyclic_order
Type of logical relation
University Schmidt, Gunther; Ströhlein, Thomas (6 December 2012). Relations and Graphs: Discrete Mathematics for Computer Scientists. Springer Science & Business
Total_relation
Argentine-born American mathematician
code restricting to total perfect codes of rectangular grid graphs (which yields an asymmetric, Penrose, tiling of the plane); in particular, Dejter characterized
Italo_Jose_Dejter
is required to find a shortest tour in a graph which visits all specified subsets of the vertices of a graph. The subsets of vertices must be disjoint
Set_TSP_problem
travel, tourism, insurance
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travel, tourism, insurance