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In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent
Quotient_graph
Mathematical result of division
(mathematics) Quotient category Quotient graph Integer division Quotient module Quotient object Quotient of a formal language, also left and right quotient Quotient
Quotient
Complete bipartite cut in a graph
is a circle graph, so testing whether a graph is a circle graph can be reduced to the same problem on the prime quotient graphs of the graph. More, when
Split_(graph_theory)
Procedures for constructing new graphs in graph theory
dual graph; medial graph; quotient graph; double graph; simplex graph; YΔ- and ΔY-transformation; Mycielskian. Binary operations create a new graph from
Graph_operations
connected graph of groups. It admits an orientation-preserving action on a tree: the original graph of groups can be recovered from the quotient graph and the
Graph_of_groups
Part of the mathematical subject of group theory
can define the natural notion of a quotient graph of groups A. The underlying graph A of A is the quotient graph X/G. The vertex groups of A are isomorphic
Bass–Serre_theory
Recursively splitting a graph into subsets of nodes
description of modular quotients and the graph decomposition they give rise to appeared in (Gallai 1967). A module of a graph is a generalization of a
Modular_decomposition
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
Mathematical concept
The set of the equivalence classes is sometimes called the quotient set or the quotient space of S {\displaystyle S} by ∼ , {\displaystyle \sim ,} and
Equivalence_class
In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space.
Graph_homology
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
Mathematics concept
countable 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
Deleting a graph edge and merging its nodes
one can identify vertices in the partition; the resulting graph is known as a quotient graph. Vertex cleaving, which is the same as vertex splitting, means
Edge_contraction
Topological space arising from a usual graph
spaces, graphs are exactly the simplicial 1-complexes and also exactly the one-dimensional CW complexes. Thus, in particular, it bears the quotient topology
Graph_(topology)
Mathematical abstraction of level sets
Reeb graph is the quotient space X /~ endowed with the quotient topology. Generally, this quotient space does not have the structure of a finite graph. Even
Reeb_graph
Mathematical group that can be generated as the set of powers of a single element
with a cyclic quotient, ending in the trivial group. Every finitely generated abelian group or nilpotent group is polycyclic. Cycle graph (group) Cyclic
Cyclic_group
Expression in calculus
In single-variable calculus, the difference quotient is usually the name for the expression f ( x + h ) − f ( x ) h {\displaystyle {\frac {f(x+h)-f(x)}{h}}}
Difference_quotient
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
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
Data organization and storage formats
graph-based data structures are used in computer science and related fields: Graph Adjacency list Adjacency matrix Graph-structured stack Scene graph
List_of_data_structures
Instantaneous rate of change (mathematics)
chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation
Derivative
Relative brain size measure
Encephalization quotient (EQ), encephalization level (EL), or just encephalization is a relative brain size measure that is defined as the ratio between
Encephalization_quotient
Unrelated vertices in graphs
the quotient of the number of vertices in G {\displaystyle G} and the independence number α ( G ) {\displaystyle \alpha (G)} . In a bipartite graph with
Independent set (graph theory)
Independent_set_(graph_theory)
Discrete subgroup in a locally compact topological group
study of homogeneous flows on the quotient spaces) and in combinatorics (through the construction of expanding Cayley graphs and other combinatorial objects)
Lattice_(discrete_subgroup)
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
Limit of the tangent line at a point that tends to infinity
oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x
Asymptote
Argentine-born American mathematician
established a canonical ordering of the vertices in a quotient graph (of each middle-levels graph under the action of a dihedral group) in one-to-one correspondence
Italo_Jose_Dejter
Algorithm related to graph distribution
G ) {\displaystyle d(G)} is the diameter. A graph is I {\displaystyle I} -bipartite, if the quotient graph of G {\displaystyle G} with I {\displaystyle
Amnesiac_flooding
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
In mathematics, straight line touching a plane curve without crossing it
The graph y = x2/3 illustrates another possibility: this graph has a cusp at the origin. This means that, when h approaches 0, the difference quotient at
Tangent
Compact Riemann surface of genus 3
way, as quotients. This tiling is uniform but not regular (it is by scalene triangles), and often regular tilings are used instead. A quotient of any tiling
Klein_quartic
Balanced complete multipartite graph
s} are the quotient and remainder of dividing n {\displaystyle n} by r {\displaystyle r} (so n = q r + s {\displaystyle n=qr+s} ), the graph is of the
Turán_graph
Mathematical theorem for algebraic structure of subgroups of free products
Bass–Serre universal covering tree for the graph of groups Y. Since H ≤ G also acts on X, consider the quotient graph of groups Z for the action of H on X.
Kurosh_subgroup_theorem
Mathematical function, inverse of an exponential function
and quotient of two positive numbers c and d were routinely calculated as the sum and difference of their logarithms. The product cd or quotient c/d came
Logarithm
On converting relations to functions of several real variables
by F ( x , y ) = 0 {\displaystyle F(x,y)=0} can also be specified as the graph of a function f {\displaystyle f} , so that for each point ( x , y ) {\displaystyle
Implicit_function_theorem
Geometric inequality applicable to any closed curve
Cauchy–Schwarz inequality. For a given closed curve, the isoperimetric quotient is defined as the ratio of its area and that of the circle having the same
Isoperimetric_inequality
Topological invariant in mathematics
into a planar graph of points and curves, in such a way that the perimeter of the missing face is placed externally, surrounding the graph obtained, as
Euler_characteristic
free discrete isometric actions of Fn on R-trees T such that the quotient metric graph T/Fn has volume 1. The Outer space X n {\displaystyle X_{n}} was
Outer_space_(mathematics)
Operation in calculus
computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally
Integral
Function type in graph theory
In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function W : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle
Graphon
Topological space that is connected
interval (see topological graph theory#Graphs as topological spaces). Then one can show that the graph is connected (in the graph theoretical sense) if and
Connected_space
Class of mathematical expression
{\displaystyle a} is the dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied
Division_by_zero
Algorithm for division of polynomials
polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that A = BQ + R, and either R = 0 or the degree
Polynomial_long_division
Result of partitioning the elements of an algebraic structure using a congruence relation
mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are
Quotient_(universal_algebra)
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
Type of mathematical expression
real variable can be represented by a graph. The graph of the zero polynomial f(x) = 0 is the x-axis. The graph of a degree 0 polynomial f(x) = a0, where
Polynomial
Type of topological space
for n ≥ 2. Any connected graph is homotopy equivalent to a rose. Specifically, the rose is the quotient space of the graph obtained by collapsing a spanning
Rose_(topology)
Mathematical operation
respect to time. On the graph of a function, the sign of the second derivative is related to the concavity of the graph. The graph of a function with a positive
Second_derivative
American mathematician
free and discrete minimal isometric actions Fn on real trees where the quotient graph has volume one. By construction the Outer space Xn is a finite-dimensional
Karen_Vogtmann
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Planar movement within a Euclidean space without rotation
normal subgroup of Euclidean group E ( n ) {\displaystyle E(n)} . The quotient group of E ( n ) {\displaystyle E(n)} by T {\displaystyle \mathbb {T} }
Translation_(geometry)
Voice type
closed quotient value (a quotient of how long the vocal folds are touching to how long the cycle of vibration lasts) than “head voice”. A closed quotient ratio
Chest_voice
Collection of objects and morphisms
category. The class of all graphs forms another concrete category, where morphisms are graph homomorphisms (i.e., mappings between graphs which send vertices
Category_(mathematics)
Discrete (i.e., incremental) version of infinitesimal calculus
properties, and applications of the difference quotient of a function. The process of finding the difference quotient is called differentiation. Given a function
Discrete_calculus
Algorithm that employs a degree of randomness as part of its logic or procedure
remarks on the theory of graphs, Bull. Amer. Math. Soc. 53 (1947), 292--294 MR8,479d; Zentralblatt 32,192. Erdös, P. (1959). "Graph Theory and Probability"
Randomized_algorithm
Type of group in abstract algebra
homogeneous spaces, and automorphism groups of graphs, such as the Higman–Sims group and the Higman–Sims graph. The elements of the symmetric group on a set
Symmetric_group
Transformations induced by a mathematical group
orbit–stabilizer theorem to count the automorphisms of a graph. Consider the cubical graph as pictured, and let G denote its automorphism group. Then
Group_action
Group that admits a formal description in terms of reflections
that the corresponding quotient group is finite. In each case, the quotient group is itself a Coxeter group, and the Coxeter graph of the affine Coxeter
Coxeter_group
Branch of geometry that studies combinatorial properties and constructive methods
polytope, unit disk graphs, and visibility graphs. Topics in this area include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams
Discrete_geometry
graph has a vertical tangent is not differentiable at the point of tangency. A function ƒ has a vertical tangent at x = a if the difference quotient used
Vertical_tangent
Function with a repeating pattern
fundamental period. Geometrically, a periodic function's graph exhibits translational symmetry. Its graph is invariant under translation in the x {\displaystyle
Periodic_function
Matrix equal to its conjugate-transpose
often exhibit Hermitian properties. In graph theory, Hermitian matrices are used to study the spectra of graphs. The Hermitian Laplacian matrix is a key
Hermitian_matrix
Algebraic structure
homomorphism, called the quotient map, canonical surjection or projection; if S {\displaystyle S} is a monoid then quotient semigroup is a monoid with
Semigroup
Pictorial representation of symmetry
of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin
Dynkin_diagram
Measurement used for rough estimate of the intelligence of an animal
inaccurate in many cases. A more complex measurement, encephalization quotient, takes into account allometric effects of widely divergent body sizes across
Brain–body_mass_ratio
Analog of the continuous Laplace operator
operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices)
Discrete_Laplace_operator
On tangency patterns of circles
whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph having a vertex for each circle, and an edge
Circle_packing_theorem
Doughnut-shaped surface of revolution
Sn, which is the quotient of the torus by the symmetric group on n letters (by permuting the coordinates). For n = 2, the quotient is the Möbius strip
Torus
Mathematical space with a notion of distance
mathematics. For example, Riemannian manifolds, normed vector spaces, and graphs may be viewed as metric spaces. In abstract algebra, the field of p-adic
Metric_space
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
Derivative of a function with multiple variables
n_{2}}}\right)_{n_{1},n_{3}}} This equality can be rearranged to have differential quotient of mole fractions on one side. Partial derivatives are key to target-aware
Partial_derivative
Study of rates of change
that this limit exists. The quotient inside the limit is the slope of a secant line through two nearby points on the graph. As h approaches zero, the secant
Differential_calculus
Construction in graph theory
In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation
McKay_graph
Topological space formed from distances
its 1-skeleton is the unit disk graph of its points. It contains a simplex for every clique in the unit disk graph, so it is the clique complex or flag
Vietoris–Rips_complex
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
Method for finding largest (or smallest) eigenvalues
x {\displaystyle r=Ax-\lambda (x)x} of a scaled gradient of a Rayleigh quotient λ ( x ) = ⟨ x , A x ⟩ / ⟨ x , x ⟩ {\displaystyle \lambda (x)=\langle x
LOBPCG
Mathematical concept for comparing objects
is a partition of the set X {\displaystyle X} . It is also called the quotient set of X {\displaystyle X} by R {\displaystyle R} . The following relations
Equivalence_relation
Branch of mathematics that studies the properties of groups
of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic
Group_theory
Reflexive and transitive binary relation
graph. A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph.
Preorder
Mathematical abelian group
graphs with even fewer entities. These include the graph with four vertices and one edge, which remains simple but loses connectivity, and the graph with
Klein_four-group
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)
Abstraction of linear independence of vectors
theory borrows extensively from the terms used in both linear algebra and graph theory, largely because it is the abstraction of various notions of central
Matroid
Abstract regular polyhedron with 3 square faces
space. From the point of view of graph theory the skeleton is a tetrahedral graph, an embedding of K4 (the complete graph with four vertices) on a projective
Hemicube_(geometry)
Branch of mathematics
tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. If the input of
Calculus
Knowledge Graph which when clicked, makes confetti explode. "panipuri( see it )" will show three types of panipuris in the Knowledge Graph, which when
List_of_Google_Easter_eggs
Type of topological space
Hausdorff, but quotient spaces of Hausdorff spaces need not be Hausdorff. In fact, every topological space can be realized as the quotient of some Hausdorff
Hausdorff_space
Index of articles associated with the same name
tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree, spanning trees of a graph formed by choosing
Random_tree
In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz
Graph_C*-algebra
Algebraic surface
icosagon (20-gon), shown here with dodecadodecahedral graph in green and its dual in violet. It is a quotient of the order-4 pentagonal tiling and its dual square
Bring's_curve
between them in the Cayley graph of Z q n {\displaystyle \mathbf {Z} _{q}^{n}} . This can also be thought of as the quotient metric resulting from reducing
Lee_distance
Topics referred to by the same term
factor group or quotient ring in abstract algebra A von Neumann algebra, with a trivial center Factor (graph theory), a spanning sub graph Any finite contiguous
Factor
Mathematical space with a notion of closeness
the quotient topology is the finest topology on Y {\displaystyle Y} for which f {\displaystyle f} is continuous. A common example of a quotient topology
Topological_space
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)
Topological space that locally resembles Euclidean space
Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the
Manifold
Non-abelian group of order eight
obtain a one-dimensional representation factoring through the 2-element quotient group G/N. The representation sends elements of N to 1, and elements outside
Quaternion_group
vertex in a graph of 3510 (= 2⋅33⋅5⋅13). These vertices are identified as conjugate 3-transpositions in the symmetry group Fi22 of the graph. The Fischer
Fischer_group
Topics referred to by the same term
over a ring that is embedded in a vector space over a field Lattice graph, a graph that can be drawn within a repeating arrangement of points Lattice-based
Lattice
the codomain with sequences in the domain. Examples include sequentially quotient maps, sequence coverings, 1-sequence coverings, and 2-sequence coverings
Sequence_covering_map
Isomorphism of an object to itself
{\displaystyle \mathbb {O} } ) is the exceptional Lie group G2. In graph theory an automorphism of a graph is a permutation of the nodes that preserves edges and
Automorphism
Type of topological space
a regular cellulation. A loopless graph is represented by a regular 1-dimensional CW-complex. A closed 2-cell graph embedding on a surface is a regular
CW_complex
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