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See searches and references containing MULTIPLICATIVE GRAPH!MULTIPLICATIVE GRAPH
Type of partial category
the compositional graph, and multiplicative graphs can be seen as strongly identitive compositional graphs. A multiplicative graph Σ {\displaystyle \Sigma
Multiplicative_graph
Mathematical operation in linear algebra
as matrix multiplication (up to a multiplicative constant), the computational complexity of matrix multiplication appears throughout numerical linear
Matrix_multiplication
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Conjecture in graph theory
has shown that square-free graphs are multiplicative. Examples of non-multiplicative graphs can be constructed from two graphs G and H that are not comparable
Hedetniemi's_conjecture
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
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
Mathematical group that can be generated as the set of powers of a single element
its inverse. Each element can be written as an integer power of g in multiplicative notation, or as an integer multiple of g in additive notation. This
Cyclic_group
Number which when multiplied by x equals 1
is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a b {\displaystyle {\tfrac {a}{b}}}
Multiplicative_inverse
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)
Longest distance between two vertices
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of
Diameter_(graph_theory)
Property of graphs that depends only on abstract structure
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations
Graph_property
Theoretical computer scientist
2008. Her dissertation, Efficient Algorithms for Path Problems in Weighted Graphs, was supervised by Guy Blelloch. After postdoctoral research at the Institute
Virginia_Vassilevska_Williams
Structure-preserving correspondence between node-link graphs
Identifying multiplicative graphs lies at the heart of Hedetniemi's conjecture. Graph homomorphisms also form a category, with graphs as objects and
Graph_homomorphism
Algorithm to multiply matrices
Graphs for Matrix Multiplication". arXiv:2212.01175 [cs.SC]. Brubaker, Ben (23 November 2022). "AI Reveals New Possibilities in Matrix Multiplication"
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Classification of algorithm
(see, for example, Reingold's algorithm for connectivity in undirected graphs). As Lipton states: This alone could be important and often is a great reason
Galactic_algorithm
Topics referred to by the same term
product or pullback Coproduct or pushout Wick product of random variables Graph product Product (Brand X album), 1979 Product (De Press album), 1982 Product
Product
Performing order of mathematical operations
is replaced with multiplication by the reciprocal (multiplicative inverse), then the associative and commutative laws of multiplication allow the factors
Order_of_operations
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel J. Mason who coined the term, is
Signal-flow_graph
Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Mathematical operation on matrices
weights of a graph, then Wk gives the distances between vertices using paths of length at most k edges, and Wn is the distance matrix of the graph. Uri Zwick
Min-plus matrix multiplication
Min-plus_matrix_multiplication
Measurement scale based on orders of magnitude
25). Exponential growth curves are often depicted on a logarithmic scale graph. The markings on slide rules are arranged in a log scale for multiplying
Logarithmic_scale
Mathematical transform
In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors
Graph_Fourier_transform
Form of data structure
A scene graph is a hierarchical data structure commonly used by vector-based graphics editing applications and modern computer games, which cascades the
Scene_graph
Graph in graph theory
In graph theory, the lexicographic product or (graph) composition G ∙ H of graphs G and H is a graph such that the vertex set of G ∙ H is the cartesian
Lexicographic product of graphs
Lexicographic_product_of_graphs
API for graph data and graph operations
via linear algebraic methods (e.g. matrix multiplication) over different semirings. The development of GraphBLAS and its various implementations is an
GraphBLAS
Node ordering for directed acyclic graphs
computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u
Topological_sorting
Two closely related models for generating random graphs
David (1997-04-01). "Brownian excursions, critical random graphs and the multiplicative coalescent". The Annals of Probability. 25 (2). doi:10.1214/aop/1024404421
Erdős–Rényi_model
Number of "holes" of a surface
Genus of orientable surfaces Planar graph: genus 0 Toroidal graph: genus 1 Double Toroidal graph: genus 2 Pretzel graph: genus 3 The non-orientable genus
Genus_(mathematics)
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
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
Diagram of behavior of finite state systems
"unfolding" originates from this multiplication of locations when producing the state graph from the program graph. A self transition is a transition
State_diagram
Norm on a vector space of matrices
} can be rescaled to be sub-multiplicative; in some books, the terminology matrix norm is reserved for sub-multiplicative norms. A matrix norm is called
Matrix_norm
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Directed graph which is also a multigraph
and multiplicative graphs can both be seen as reflexive quivers with additional structure. ADE classification Adhesive category Assembly theory Graph algebra
Quiver_(mathematics)
Creating a new graph from an existing graph
computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It
Graph_rewriting
fast multiplication algorithm for large integers Toom–Cook multiplication: (Toom3) a multiplication algorithm for large integers Multiplicative inverse
List_of_algorithms
Assigning directions to the edges of an undirected graph
In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph. A
Orientation_(graph_theory)
Specific element of an algebraic structure
respect to multiplication is called a multiplicative identity (often denoted as 1). These need not be ordinary addition and multiplication—as the underlying
Identity_element
Optimization technique
As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Graph without four-vertex star subgraphs
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the
Claw-free_graph
Graph without triples of adjacent vertices
area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently
Triangle-free_graph
Mathematical function, inverse of an exponential function
channels. Zech's logarithm is related to the discrete logarithm in the multiplicative group of non-zero elements of a finite field. Further logarithm-like
Logarithm
French mathematician (1905–1979)
category theory, where he introduced the concepts of sketch, of multiplicative graph, and of strict 2-category. His collected works, edited by his wife
Charles_Ehresmann
Embedding of the circle in three dimensional Euclidean space
mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional
Knot_(mathematics)
Association of one output to each input
a real function f : x ↦ f ( x ) {\displaystyle f:x\mapsto f(x)} its multiplicative inverse x ↦ 1 / f ( x ) {\displaystyle x\mapsto 1/f(x)} is also a real
Function_(mathematics)
Mathematical abelian group
{R} ^{\times }} denotes the multiplicative group of non-zero reals and R + {\displaystyle \mathbb {R} ^{+}} the multiplicative group of positive reals, then
Klein_four-group
Problem in computational complexity theory
linear time. Determining s-t reachability for a (worst-case) dynamic graph on a graph with n {\displaystyle n} nodes and m ≤ n 2 {\displaystyle m\leq n^{2}}
Online matrix-vector multiplication problem
Online_matrix-vector_multiplication_problem
Task of computing complete subgraphs
vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what
Clique_problem
Construction in combinatorial group theory
theory, the Schreier coset graph is a graph associated with a group G, a generating set of G, and a subgroup of G. The Schreier graph encodes the abstract structure
Schreier_coset_graph
Mathematical function, denoted exp(x) or e^x
\exp(x+y)=\exp(x)\cdot \exp(y)} and maps the additive identity 0 to the multiplicative identity 1. The same equation is satisfied by other continuous functions
Exponential_function
Four-dimensional number system
and the component-wise scalar multiplication λ(a+b𝐢+c𝐣+d𝐤)=λa+(λb)𝐢+(λc)𝐣+(λd)𝐤. A multiplicative group structure, called the Hamilton product
Quaternion
Copy of a directed graph with redundant edges removed
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges
Transitive_reduction
Number of integers coprime to and less than n
1 ) = 1 {\displaystyle \gcd(1,1)=1} . Euler's totient function is a multiplicative function, meaning that if two numbers m {\displaystyle m} and n {\displaystyle
Euler's_totient_function
List of unsolved computational problems
every weakly normalizing pure type system also strongly normalizing? Is multiplicative-exponential linear logic decidable? Is the Aanderaa–Karp–Rosenberg conjecture
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Least-weight tree connecting graph vertices
graph theory, a minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that
Minimum_spanning_tree
Branch of elementary mathematics
by that number. For instance, 48÷8=48×18. The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that
Arithmetic
Index of articles associated with the same name
approximation in Big O notation Z-order (curve), a space-filling curve Multiplicative order in modular arithmetic Order of operations Orders of magnitude
Order_(mathematics)
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)
Property of two varying quantities with a constant ratio
proportion) if each of the variables is directly proportional to the multiplicative inverse (reciprocal) of the other, or equivalently if their product
Proportionality_(mathematics)
Arithmetic operation
invertible elements in a multiplicative monoid, that is, an algebraic structure, with an associative multiplication and a multiplicative identity denoted 1
Exponentiation
In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units
Motion_graphs_and_derivatives
Identity obeyed by many special functions related to the gamma function
obeying the multiplication theorem from any totally multiplicative function. Let f ( n ) {\displaystyle f(n)} be totally multiplicative; that is, f (
Multiplication_theorem
Mathematical concept
notation f −1(x) might be misunderstood, (f(x))−1 certainly denotes the multiplicative inverse of f(x) and has nothing to do with the inverse function of f
Inverse_function
Number with a real and an imaginary part
an additive inverse −z and every nonzero complex number z has a multiplicative inverse 1/z; the complex numbers form a field, much as the rational
Complex_number
definition. There are still other definitions in the research literature. Multiplicative graph Adámek, Jiří; Rosický, Jiří (1994), Locally Presentable and Accessible
Sketch_(mathematics)
Topics referred to by the same term
Integer partition, a way to write an integer as a sum of other integers Multiplicative partition, a way to write an integer as a product of other integers
Partition
Topics referred to by the same term
RNG may refer to: Random number generator Relative neighborhood graph, an undirected graph used in computational geometry RELAX NG, an XML schema language
RNG
and the multiplicative Zagreb indices Π 1 ( G ) {\displaystyle \Pi _{1}(G)} and Π 2 ( G ) {\displaystyle \Pi _{2}(G)} . Highly irregular graph Gutman,
Stepwise_irregular_graph
Unsolved problem in extremal graph theory
mathematics What is the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs
Zarankiewicz_problem
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
of Journal of Graph Algorithms and Applications and Information and Computation. Fürer, Martin (2009), "Faster Integer Multiplication", SIAM Journal
Martin_Fürer
All even-degree subgraphs of a graph
multiplication by the scalar 1 is the multiplicative identity operation, and multiplication by the scalar 0 takes every element to the edgeless graph
Cycle_space
Dimensionality reduction of graph-based semantic data objects [machine learning task]
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine
Knowledge_graph_embedding
unweighted, connected graphs. It solves the problem in O ( V ω log V ) {\displaystyle O(V^{\omega }\log V)} expected time for a graph with V {\displaystyle
Seidel's_algorithm
Planar movement within a Euclidean space without rotation
graph consisting of points ( x , f ( x − a ) ) {\displaystyle (x,f(x-a))} . Each point ( x , y ) {\displaystyle (x,y)} of the original graph corresponds
Translation_(geometry)
Branch of discrete mathematics
right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas
Combinatorics
Graph with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
Branch of mathematics
existence of multiplicative identity elements. A ring without multiplicative identity is sometimes called a rng. This means that multiplication and addition
Algebra
Theory of attitude change
the signs shows that the person will perceive imbalance (a negative multiplicative product) in this relationship, and will be motivated to correct the
Balance_theory
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Property of some mathematical operations
Commutative diagram Commutative (neurophysiology) Commutator Commuting graph Commuting probability Particle statistics (for commutativity in physics)
Commutative_property
Polynomial whose roots are the eigenvalues of a matrix
characteristic polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency
Characteristic_polynomial
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
Logical connective AND
a part of the flag. AND gate – Digital logic gate type And-inverter graph – Graph representing an implementation of the logical functionality of a network
Logical_conjunction
Ring that is also a vector space or a module
commutative ring. In this article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras
Associative_algebra
Analog of the continuous Laplace operator
V\rightarrow R} be a potential function defined on the graph. Note that P can be considered to be a multiplicative operator acting diagonally on ϕ {\displaystyle
Discrete_Laplace_operator
Complexity class of approximable problems
have efficient algorithms that can find an answer within some fixed multiplicative factor of the optimal answer. An approximation algorithm is called an
APX
Reasoning about comparative relationships
Proportional reasoning is the ability to understand and reason about multiplicative relationships between quantities, such as ratios, rates, fractions,
Proportional_reasoning
Concept in machine learning
designs of machine learning in the form of tensor graphs. This leads to new architectures, such as tensor-graph convolutional networks (TGCN), which identify
Tensor_(machine_learning)
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
2026 release of AI-generated mathematical solutions
Erdős–Turán conjecture is true. The crossing numbers of complete graphs and complete bipartite graphs were determined. A proof of the Hilbert–Smith conjecture
OpenAI bulk release of mathematical papers
OpenAI_bulk_release_of_mathematical_papers
Natural number
cubic 3-connected bipartite graph is Hamiltonian. Horton disproved the conjecture some years earlier with the Horton graph, but that was larger at 92 vertices
54_(number)
Transformations induced by a mathematical group
multiplication. The automorphism group of a vector space (or graph, or group, or ring ...) acts on the vector space (or set of vertices of the graph,
Group_action
Real function with secant line between points above the graph itself
line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two points . Equivalently
Convex_function
Estimate of time taken for running an algorithm
(addition, subtraction, multiplication, division, and comparison) can be done in polynomial time. Maximum matchings in graphs can be found in polynomial
Time_complexity
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 theory problem: find a matching containing the most edges
In graph theory, a maximum-cardinality matching is a special kind of subgraph useful in many computational contexts. Given a graph G, a matching is a
Maximum-cardinality_matching
Topics referred to by the same term
the mapped entities, in particular: Graph isomorphism a mapping that preserves the edges and vertices of a graph Group isomorphism a mapping that preserves
Isomorphism_(disambiguation)
Device used for calculations
calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher-dimensional
Calculator
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MULTIPLICATIVE GRAPH
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MULTIPLICATIVE GRAPH
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MULTIPLICATIVE GRAPH
MULTIPLICATIVE GRAPH
MULTIPLICATIVE GRAPH
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