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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
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
Operation in graph theory
In graph theory, the tensor 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 vertices
Tensor_product_of_graphs
Binary operation in graph theory
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they
Strong_product_of_graphs
Procedures for constructing new graphs in graph theory
zig-zag graph product; graph product based on other products: rooted graph product: it is an associative operation (for unlabelled but rooted graphs), corona
Graph_operations
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
Topics referred to by the same term
mathematical products Fibre product or pullback Coproduct or pushout Wick product of random variables Graph product Product (Brand X album), 1979 Product (De Press
Product
Binary operation performed on graphs
In mathematical graph theory, the rooted product (or comb product) of a graph G and a rooted graph H is defined as follows: take |V(G)| copies of H, and
Rooted_product_of_graphs
Binary operation in graph theory
In graph theory, the zig-zag product of regular graphs G , H {\displaystyle G,H} , denoted by G ∘ H {\displaystyle G\circ H} , is a binary operation which
Zig-zag_product
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
American computer scientist
a new type of graph product, called the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its
Salil_Vadhan
Function graph representing factorization
distributions through the sum–product algorithm. One of the important success stories of factor graphs and the sum–product algorithm is the decoding of
Factor_graph
Graph whose embedding in a Euclidean space forms a regular tiling
Cartesian product of a number of complete graphs. A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the
Lattice_graph
Mathematical set formed from two given sets
Cartesian product of graphs is not a product in the sense of category theory. Instead, the categorical product is known as the tensor product of graphs. Axiom
Cartesian_product
Binary operation on mathematical graphs
In graph theory, the replacement product of two graphs is a graph product that can be used to reduce the degree of a graph while maintaining its connectivity
Replacement_product
Vertices connected in pairs by edges
of graphs, cartesian product of graphs, tensor product of graphs, strong product of graphs, lexicographic product of graphs, series–parallel graphs. In
Graph_(discrete_mathematics)
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Graph of king moves on a chessboard
also be constructed as the strong product of two path graphs. For an n × m {\displaystyle n\times m} king's graph the total number of vertices is n m
King's_graph
Graph of chess rook moves
mathematics of graphs through their alternative constructions: rook's graphs are the Cartesian product of two complete graphs, and are the line graphs of complete
Rook's_graph
In graph theory, the corona product of graphs G and H, denoted G ∘ H {\displaystyle G\circ H} , can be obtained by taking one copy of G, called the center
Corona_product
product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph
Dot product representation of a graph
Dot_product_representation_of_a_graph
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
Conjecture in graph theory
1966, concerns the connection between graph coloring and the tensor product of graphs. This conjecture states that χ ( G × H ) = min { χ ( G ) , χ ( H )
Hedetniemi's_conjecture
Planar, undirected graph with 2n vertices and 3n-2 edges
Cartesian product of two path graphs, one of which has only one edge: Ln = Pn □ P2. By construction, the ladder graph Ln is isomorphic to the grid graph G2,n
Ladder_graph
Cartesian product of complete graphs
is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs Kq. In some cases, Hamming graphs may be considered more
Hamming_graph
In polytope theory, the edge graph (also known as vertex-edge graph or just graph) of a polytope is a combinatorial graph whose vertices and edges correspond
Graph_of_a_polytope
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
Proposition on the domination number of Cartesian products of graphs
mathematics In graph theory, Vizing's conjecture concerns a relation between the domination number and the cartesian product of graphs. This conjecture
Vizing's_conjecture
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)
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
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Graphs formed by a hypercube's edges and vertices
single digit. It is the n {\displaystyle n} -fold Cartesian product of the two-vertex complete graph, and may be decomposed into two copies of Q n − 1 {\displaystyle
Hypercube_graph
Distance-regular graph with 56 vertices
representation of the Gosset graph, two vertices are at distance two when their inner product is −8 and at distance three when their inner product is −24 (which is
Gosset_graph
Austrian mathematician (born 1941)
mathematician working mainly in graph theory. He is known for his work on graph products, and authored the books Product Graphs: Structure and Recognition
Wilfried_Imrich
Mathematical operation on matrices
n × n {\displaystyle n\times n} matrix containing the edge weights of a graph, then W k {\displaystyle W^{k}} gives the distances between vertices using
Min-plus matrix multiplication
Min-plus_matrix_multiplication
(“Entropy waves, the zig-zag graph product, and new constant-degree expanders”, 2002) in order to conveniently define the zig-zag product and prove its properties
Rotation_map
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
Family of graphs with 2n nodes and n(n-1) edges
complete graph, as the tensor product Kn × K2, as the complement of the Cartesian direct product of Kn and K2, or as a bipartite Kneser graph Hn,1 representing
Crown_graph
Graph with sign-labeled edges
graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of
Signed_graph
Graph where every edge is in one triangle
locally linear graphs include the triangular cactus graphs, the line graphs of 3-regular triangle-free graphs, and the Cartesian products of smaller locally
Locally_linear_graph
Geometric graph with unit edge lengths
or cactus graph may be realized as a unit distance graph. Any Cartesian product of unit distance graphs produces another unit distance graph; however,
Unit_distance_graph
Baseball statistics website
partners including ESPN, SB Nation and Fanhouse. FanGraphs creates several products: The FanGraphs homepage, which contains articles, statistical reports
FanGraphs
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and
Rooted_graph
Mathematical game played on a graph
is a wheel graph on n vertices. Unsolved problem in mathematics Is the pebbling number of a Cartesian product of graphs at most the product of the pebbling
Graph_pebbling
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
Robustness of graph perfect matchings
In graph theory, a branch of mathematics, the matching preclusion number of a graph G {\displaystyle G} , denoted m p ( G ) {\displaystyle \mathrm {mp}
Matching_preclusion
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
Topics referred to by the same term
Corona algebra (or corona) of a C*-algebra Corona graph product, a kind of binary operation on two graphs Corona set (or corona), of a topological space
Corona
Mathematical group that can be generated as the set of powers of a single element
each product of an element with a generator. In the case of a finite cyclic group, with its single generator, the Cayley graph is a cycle graph, and for
Cyclic_group
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
Curve for failure rates over time
curve is a failure rate graph that curves up at both ends, similar in shape to a bathtub. The term can also apply to any graph with this shape. Many but
Bathtub_curve
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
Representation of a mathematical function
product X × Y {\displaystyle X\times Y} . In the definition of a function in terms of set theory, it is common to identify a function with its graph,
Graph_of_a_function
In structure mining, a graph kernel is a kernel function that computes an inner product on graphs. Graph kernels can be intuitively understood as functions
Graph_kernel
unsolved problems in mathematics In graph theory, an overfull graph is a graph whose size is greater than the product of its maximum degree and half of
Overfull_graph
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
Graph representing connectivity between cliques of another graph
simplex graph of a complete graph is a hypercube graph, and the simplex graph of a cycle graph of length four or more is a gear graph. The simplex graph of
Simplex_graph
Theorem relating continuity to graphs
the graph of f {\displaystyle f} is closed if Γ f {\displaystyle \Gamma _{f}} is a closed subset of X × Y {\displaystyle X\times Y} (with the product topology)
Closed_graph_theorem
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
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
Set of unordered triples from a vertex set
the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been
Two-graph
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
Planar graph with 4 nodes and 5 edges
mathematical field of graph theory, the diamond graph is a planar, undirected graph with 4 vertices and 5 edges. It consists of a complete graph K 4 {\displaystyle
Diamond_graph
2018 mathematics book by Marcus Schaefer
concerns other special classes of graphs including graph products (especially products of cycle graphs) and hypercube graphs. After a third chapter relating
Crossing_Numbers_of_Graphs
Node labeling problem in graph theory
In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number
Graph_bandwidth
Graph of short distances in another graph
square of G, G3 is called the cube of G, etc. Graph powers should be distinguished from the products of a graph with itself, which (unlike powers) generally
Graph_power
Algebraic operation on coordinate vectors
Cauchy–Schwarz inequality Cross product Dot product representation of a graph Euclidean norm, the square-root of the self dot product Matrix multiplication Metric
Dot_product
Upper bound on a graph's Shannon capacity
In graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász
Lovász_number
Property of functions in topology
is a closed subset of the product space X × Y. This property is studied because there are many theorems, known as closed graph theorems, giving conditions
Closed_graph_property
makes extensive use of graphs to better illustrate the economic principles and trends it is attempting to explain. Those graphs have specific qualities
Economic_graph
graphs, as Cartesian products of any number of complete graphs K 2 {\displaystyle K_{2}} , are integral. The line graph of a regular integral graph is
Integral_graph
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Vertex adjacent to all others in a graph
In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating
Universal_vertex
Family of infinite discrete groups
r-1} , with the free product and direct product as the extreme cases. A generalization of this construction is called a graph product of groups. A right-angled
Artin–Tits_group
Trail in a graph that visits each edge once
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)
Eulerian_path
16-regular graph with 27 vertices and 216 edges
Schläfli graph; two vertices are adjacent if and only if the corresponding two vectors have 1 as their inner product. Alternately, this graph can be seen
Schläfli_graph
Graph coloring variant in graph theory
In graph theory, a packing coloring (also called a broadcast coloring) is a type of graph coloring where vertices are assigned colors (represented by positive
Packing_coloring
Index of articles associated with the same name
the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. The Martin polynomial, used by Pierre
Graph_polynomial
Slovenian mathematician
Tomaž Pisanski. Klavžar's research concerns graph products, metric graph theory, chemical graph theory, graph domination, and the Tower of Hanoi. Together
Sandi_Klavžar
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
Path in a graph that visits each vertex exactly once
the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly
Hamiltonian_path
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
Graph with a prism as its skeleton
of generalized Petersen graphs, with parameters GP(n,1). They may also be constructed as the Cartesian product of a cycle graph with a single edge. As
Prism_graph
Maximal subgraph whose vertices can reach each other
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph
Component_(graph_theory)
Undirected, connected, and acyclic graph
In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected
Tree_(graph_theory)
Directed graph representing dependencies
mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other
Dependency_graph
Graph database product by Amazon
Amazon Neptune is a managed graph database product published by Amazon.com. It is used as a web service and is part of Amazon Web Services (AWS). It was
Amazon_Neptune
Type of graph related to pursuit–evasion
In graph theory, a cop-win graph is an undirected graph on which the pursuer (cop) can always win a pursuit–evasion game against a robber, with the players
Cop-win_graph
Used to define marginal product and to distinguish allocative efficiency
concepts of mainstream neoclassical theories, used to define marginal product and to distinguish allocative efficiency, a key focus of economics. One
Production_function
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
One of two types of graph
That is, it is a Cartesian product of a star and a single edge. The 7-page book graph of this type provides an example of a graph with no harmonious labeling
Book_(graph_theory)
Vector space with generalized dot product
mathematics, an inner product space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in
Inner_product_space
In graph theory, a stepwise irregular graph (or SI graph) is a graph in which the degrees of any two adjacent vertices differ by exactly one. This concept
Stepwise_irregular_graph
Mathematical operation in linear algebra
semiring is also a common choice for graph shortest path problems. Even in the case of matrices over fields, the product is not commutative in general, although
Matrix_multiplication
Mathematical model used by graph-oriented databases
A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated
Property_graph
Degrees of separation from Paul Erdős
McEliece, Robert James; Taylor, Herbert (1971). "Ramsey bounds for graph products" (PDF). Pacific Journal of Mathematics. 37 (1): 45–46. doi:10.2140/pjm
Erdős_number
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Construction for generating graphs for modeling systems
a small base graph by iterating the Kronecker product. A variety of generalizations of Kronecker graphs exist. The Graph500 benchmark for supercomputers
Kronecker_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes
Circulant_graph
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travel, tourism, insurance