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Binary operation in graph theory
In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism. It is one
Modular_product_of_graphs
Binary operation on graphs
graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H
Graph_product
Mathematical group that can be generated as the set of powers of a single element
other sets of generators as well. The Cayley graphs of cyclic groups with arbitrary generator sets are called circulant graphs. These graphs may be represented
Cyclic_group
Task of computing complete subgraphs
use of the modular product of graphs to reduce the problem of finding the maximum common induced subgraph of two graphs to the problem of finding a maximum
Clique_problem
Methodic assignment of colors to elements of a graph
for signed graphs and gain graphs. Colored matroid Critical graph Graph coloring game Graph homomorphism Hajós construction Mathematics of Sudoku Multipartite
Graph_coloring
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 or
Glossary_of_graph_theory
Operation that combines groups
theory that the modular group is isomorphic to the free product of cyclic groups of orders 4 and 6 amalgamated over a cyclic group of order 2. If G
Free_product
standard graph products, but not the modular product of graphs. The string graphs of bounded degree. In every hereditary family of graphs of bounded twin-width
Twin-width
Digital record required under EU law for product compliance, safety, and sustainability
A Digital Product Passport (DPP), sometimes referred to as the product’s technical file, is a digital record mandated by EU law that consolidates essential
EU_Digital_Product_Passport
Measure of capacity of a communications channel defined from a graph
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named
Shannon_capacity_of_a_graph
Topics referred to by the same term
discipline of designing complex devices using separately designed sub-components Modular function deployment, a method in systems engineering and product development
Module
Graph with a median for each three vertices
{\displaystyle Q} of the given median graph. The only regular median graphs are the hypercubes. Every median graph is a modular graph. The modular graphs are a class
Median_graph
In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs G and H is a graph that is an induced subgraph of both
Maximum common induced subgraph
Maximum_common_induced_subgraph
Approximate nearest neighbor search algorithm
locality-sensitive hashing and product quantization. HNSW builds on research into small-world networks and navigable graphs. In a small-world graph, most nodes can be
Hierarchical navigable small world
Hierarchical_navigable_small_world
Type of lattice in mathematical order theory
described the free modular lattice generated by three elements, a lattice with 28 elements (see picture). Modular graph, a class of graphs that includes the
Modular_lattice
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Soviet Ukrainian mathematician (1937–2017)
domination number of cartesian products of graphs,[V68] and the 1974 definition of the modular product of graphs as a way of reducing subgraph isomorphism
Vadim_G._Vizing
Mathematical concept
A modular elliptic curve is an elliptic curve E that admits a parametrization X0(N) → E by a modular curve. This is not the same as a modular curve that
Modular_elliptic_curve
Software design structured around a node graph
problems many node graphs architectures restrict themselves to a subset of graphs known as directed acyclic graphs. The use of node graph architecture in
Node_graph_architecture
Type of group in group theory
} ) of Lubotzky and Zimmer can be used to construct expander graphs (Margulis), or even Ramanujan graphs (Lubotzky-Phillips-Sarnak). Such graphs are known
Arithmetic_group
Graphical representation of energy flows in physical systems
analogy is one example of a physical analogy. Bond graphs use the concept of analogous power conjugate variables whose product is energy flow, or power;
Bond_graph
Topics referred to by the same term
common divisor of two numbers Equivalence class congruence, especially for modular arithmetic or modulo an ideal A higher order derivative in Lagrange's notation
Math_symbol_brackets
Topic in group theory
Wreath products arise naturally in the symmetries of complete rooted trees and their graphs. For example, the repeated (iterated) wreath product S 2 ≀
Wreath_product
Natural number
In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with
5
for planar graphs or polyhedra: v − e + f = 2, a special case of the Euler characteristic in topology Euler's formula for the critical load of a column:
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Deep learning software
create complex task-tailored graphs. Simpler modules like Linear, Tanh and Max make up the basic component modules. This modular interface provides first-order
Torch_(machine_learning)
example the Hecke operators of modular form theory may be considered as correspondences of modular curves. However, the definition of a correspondence in algebraic
Correspondence (algebraic geometry)
Correspondence_(algebraic_geometry)
Unsolved problem in mathematics
conjecture concerning the growth rate of coefficients of modular forms and more generally, automorphic forms. The name of the conjecture comes from Srinivasa
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Bioinformatics software platform
analyse and visualise graphs in JavaScript environments, like a browser. Cytoscape was originally created at the Institute of Systems Biology in Seattle
Cytoscape
Algebraic curve in mathematics
of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K2, the Cartesian product of
Elliptic_curve
Project for a modular smartphone by Google
Project Ara was a modular smartphone project under development by Google. The project was originally headed by the Advanced Technology and Projects team
Project_Ara
Operating system
first product was the IWS (Integrated Workstation) based on the Intel 8086 processor, which had CTOS as its operating system. This was a modular operating
Convergent Technologies Operating System
Convergent_Technologies_Operating_System
Natural number
number. There are 728 cubes of edge length 1 required to make a hollow cube of edge length 12.There are 728 connected graphs on 5 labelled vertices. 728
700_(number)
Graph based kernel networking subsystem of FreeBSD and DragonFly BSD
provides support for L2TP, PPTP, ATM, Bluetooth using a modular set of nodes that are the graph. Netgraph has also been ported on other Operating Systems:
Netgraph
Finite group
"modular group of order 16", as its lattice of subgroups is modular. In this article this group will be called the modular maximal-cyclic group of order
Quasidihedral_group
Open source modular construction model
According to Lommee, the OpenStructures project explores the possibility of a modular system where "everyone designs for everyone." OpenStructures is developing
OpenStructures
ISO standard
integration — Product data representation and exchange) is a family of ISO standards for computer-interpretable representation (description) and exchange of product
ISO_10303
functions Theta functions Neville theta functions Modular lambda function Closely related are the modular forms, which include J-invariant Dedekind eta function
List of mathematical functions
List_of_mathematical_functions
The identity element in the cycle graphs is represented by the black circle. The lowest order for which the cycle graph does not uniquely represent a group
List_of_small_groups
On linear-time algorithms for graph logic
study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be
Courcelle's_theorem
Family of random graph models
self-loops or multi-edges. Multi-edge graphs: Graphs allowing multiple edges between the same pair of nodes. Loopy graphs: Graphs that include self-loops (edges
Configuration_model
Overview of and topical guide to discrete mathematics
methods Graph theory – Area of discrete mathematics a study of graphs – Vertices connected in pairs by edges Mathematical logic – Subfield of mathematics
Outline of discrete mathematics
Outline_of_discrete_mathematics
Matrix group
subgroups of 2 × 2 matrices are fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence
Congruence_subgroup
Lattice whose elements are the subgroups of a given group
the modular property of groups (Aschbacher 2000) or (Dedekind's) modular law (Robinson 1996, Cohn 2000). Since for two normal subgroups the product is
Lattice_of_subgroups
Series of programmable logic controllers
stored in the form of a software program in the memory of a Central Processing Unit-type control system. The automation system is modular and, in addition
Simatic
Group of symmetries of a regular polygon
\end{aligned}}} In all cases, addition and subtraction of subscripts are to be performed using modular arithmetic with modulus n {\displaystyle n} . Centering
Dihedral_group
Integer that is a perfect square modulo some integer
residues. Paley graphs are dense undirected graphs, one for each prime p ≡ 1 (mod 4), that form an infinite family of conference graphs, which yield an
Quadratic_residue
Isotope of scandium
J. (2023-02-28). "Engineering a modular 44Ti/44Sc generator: eluate evaluation in preclinical models and estimation of human radiation dosimetry". EJNMMI
Scandium-44
algorithm Sparse graph code Syndrome decoding Tanner graph Ternary Golay code Tiger (hash function) Transverse redundancy check Triple modular redundancy Turbo
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
Branch of mathematics that studies the properties of groups
area makes use of the connection of graphs via their fundamental groups. A fundamental theorem of this area is that every subgroup of a free group is
Group_theory
Type of group in abstract algebra
widely studied because of their importance in understanding group actions, homogeneous spaces, and automorphism groups of graphs, such as the Higman–Sims
Symmetric_group
Sporadic simple group
permutation group on the Hall–Janko graph of 100 points, the stabilizer of one point being a subgroup with two other orbits of lengths 36 and 63. Inspired by
Higman–Sims_group
Format for expressing RDF statements in HTML documents
content. Self Containment – the HTML and the RDF are separated Schema Modularity – the attributes are reusable Additionally RDFa may benefit web accessibility
RDFa
Sporadic simple group
a subgroup of 2E6(22). All the ordinary and modular character tables of Fi22 have been computed. Hiss & White (1994) found the 5-modular character table
Fischer_group_Fi22
September 10, 2016) was a Russian mathematician who contributed to the theory of modular forms, computational complexity theory, algebraic combinatorics and p-adic
Sergei_Evdokimov
Matrix of binary truth values
an adjacency matrix in graph theory: non-symmetric matrices correspond to directed graphs, symmetric matrices to ordinary graphs, and a 1 on the diagonal
Logical_matrix
German electronic musical instrument manufacturer
Palm Products GmbH (commonly abbreviated to PPG) was a manufacturer of audio synthesizers. Founded and owned by Wolfgang Palm, PPG was located in Hamburg
Palm_Products_GmbH
Mathematics concept
{\displaystyle G} can be written in exactly one way as a product of finitely many elements of S {\displaystyle S} and their inverses (disregarding trivial
Free_group
of databases, transaction processing (transaction management), and other transactional distributed applications, global serializability (or modular serializability)
Global_serializability
{p}}} for every prime number p and every integer a (see modular arithmetic). Some of the proofs of Fermat's little theorem given below depend on two simplifications
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
Classification of computer architectures
this, programs are represented as graphs of expressions, which are dynamically updated as reduction proceeds. Graph nodes may represent values, operations
Duncan's_taxonomy
Natural number
is also the number of cubic inches in a cubic foot. 1728 is the cube of 12, and therefore equal to the product of the six divisors of 12 (1, 2, 3, 4, 6
1728_(number)
American mathematician
group actions on trees and studying the subgroup structure of the fundamental groups of graphs of groups. The first paper in this direction was written by
John_R._Stallings
Examining the embedded components of software
call graphs with dynamic instrumentation to improve the performance of false positive elimination. This modular approach addresses limitations of purely
Software_composition_analysis
bit strings of length N, and group operations are performed by an oracle (the "black box"). These operations include: taking a product g·h of elements g
Black_box_group
Number of partitions of an integer
sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic
Partition function (number theory)
Partition_function_(number_theory)
US technology company
genotyping and Genome-Wide Association Studies (GWAS). Its first major product, Exemplar Analytics, integrated over 50 algorithms for complex genetic
Sapio_Sciences
Concept in machine learning
of tensors has enabled higher-level designs of machine learning in the form of tensor graphs. This leads to new architectures, such as tensor-graph convolutional
Tensor_(machine_learning)
The list of IBM products is a partial list of products, services, and subsidiaries of International Business Machines (IBM) Corporation and its predecessor
List_of_IBM_products
Sporadic simple group
has a rank 3 action on a graph of 31671 vertices corresponding to 3-transpositions, with point stabilizer the double cover of the Fischer group Fi22. It
Fischer_group_Fi23
generated by a conjugacy class of elements of order 2, called 'Fischer transpositions' or 3-transpositions. The product of any two distinct transpositions
Fischer_group
The following is a list of products, services, and apps provided by Google. Google Pixel – smartphones, tablets, laptops, earbuds, and other accessories
List_of_Google_products
Web application framework
application framework developed by JBoss, a division of Red Hat. Seam 3 provides a modular set of extensions to the CDI programming model. Seam's mission
JBoss_Seam
Sporadic simple group
leading to a permutation representation of degree 315. It has a modular representation of dimension six over the field of four elements; if in characteristic
Janko_group_J2
Standard representation of a mathematical object
from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism: to test whether two graphs G and H are isomorphic
Canonical_form
Transformations induced by a mathematical group
corresponds to disjoint union, and multiplication to Cartesian product. The trivial action of any group G on any set X is defined by g ⋅ x = x for all g in
Group_action
Group of even permutations of a finite set
group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree n, or the
Alternating_group
German-American software firm
managing the performance of software used in microservice architectures, and permits 3D visualisation of performance through graphs generated using machine
Instana
Structural analysis of a network
probabilities of the potential new states are unequal. Biased random walks on a graph provide an approach for the structural analysis of undirected graphs in order
Biased_random_walk_on_a_graph
System to predict users' preferences
including the selection of a product, musical selection, or online news source to read. Recommender systems usually make use of either or both collaborative
Recommender_system
line Antichain Strict order Hasse diagram Directed acyclic graph Duality (order theory) Product order Greatest element (maximum, top, unit), Least element
List_of_order_theory_topics
Non-abelian group of order eight
group D4, but a different structure, as shown by their Cayley and cycle graphs: In the diagrams for D4, the group elements are marked with their action
Quaternion_group
Sporadic simple group
MR 0249500 Ryba, A. J. E. (1988), "Calculation of the 7-modular characters of the Held group", Journal of Algebra, 117 (1): 240–255, doi:10.1016/0021-8693(88)90252-9
Held_group
Method of representing systems
the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930s-1950s the study of random graphs were developed. During
Biological_network
Presentation and data management in software systems
Server-side Front-end web development Client–server model Out-of-box experience Modular programming Observer pattern Publish–subscribe pattern Pull technology
Front_end_and_back_end
generating a variety of graphs from raw data PSPP – A free software alternative to IBM SPSS Statistics R – free implementation of the S (programming language)
List_of_statistical_software
Type of sub-graph
more, can be represented as graphs, which include a wide variety of subgraphs.[citation needed] Network motifs are sub-graphs that repeat themselves in
Network_motif
Branch of elementary mathematics
perform calculations. There are many other types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result in a number
Arithmetic
Mathematical abelian group
below. It is also the automorphism group of some other graphs with even fewer entities. These include the graph with four vertices and one edge, which remains
Klein_four-group
Sporadic simple group
Ree group 2F4(2), the automorphism group of the Tits group. This representation implies a strongly regular graph srg(4060, 2304, 1328, 1280). That is, each
Rudvalis_group
Sporadic simple group
representations of the Janko group J1 are 1, 56, 56, 76, 76, 77, 77, 77, 120, 120, 120, 133, 133, 133, 209 (sequence A003904 in the OEIS). Janko found a modular representation
Janko_group_J1
Bound lattice in which every element has a complement
to a complement. An orthocomplemented lattice satisfying a weak form of the modular law is called an orthomodular lattice. In bounded distributive lattices
Complemented_lattice
Mathematical proof about the permanent of matrices
single hard instance of some other problem in #P is reduced to computing the permanent of a sequence of multiple graphs, each of which could potentially
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
wall. As of 2023, designers were attempting to make the tiles more modular, like Legos. Pre-painted pieces make up the majority of the products sold, however
Dwarven_Forge
Mathematical concept
has center {1, −1} of order 2, and its upper central series is {1}, {1, −1}, Q8; so it is nilpotent of class 2. The direct product of two nilpotent groups
Nilpotent_group
Degree of connectedness within a graph
that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are
Centrality
Notation to express cause and effect
exist several forms of causal diagrams including Ishikawa diagrams, directed acyclic graphs, causal loop diagrams, why-because graphs (WBGs), and diagrams
Causal_notation
Game engine
place of PhysX. Added in UE5.2, the engine introduced a new material creation system named Substrate, offering more versatile and modular authoring of materials
Unreal_Engine_5
Decision tracking and managing method
Standardization and modularization driven by minimizing overall process effort." Computer-Aided Design, 38(5):405-416 T. Browning: "Modeling Impacts of Process Architecture
Design_structure_matrix
Type of mathematical expression
sum of a finite number of non-zero terms. Each term consists of the product of a number – called the coefficient of the term – and a finite number of indeterminates
Polynomial
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MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
MODULAR PRODUCT-OF-GRAPHS
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