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Extension of the RDF data model
Named graphs are a key concept of Semantic Web architecture in which a set of Resource Description Framework statements (a graph) are identified using
Named_graph
4-regular undirected graph in mathematics
mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after Neil Robertson
Robertson_graph
Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12
List_of_graphs
Cubic graph with 10 vertices and 15 edges
problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no
Petersen_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Graph with oriented edges
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed
Directed_graph
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
ASCII-based file format for describing graphs
Graph Modeling Language (GML) is a hierarchical ASCII-based file format for describing graphs. It has been also named Graph Meta Language. A simple graph
Graph_Modelling_Language
Graph with an Archimedean solid as its skeleton
field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all
Archimedean_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
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
Regular graph with girth more than twice its diameter
Does a Moore graph with girth 5 and degree 57 exist? More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth
Moore_graph
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
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
Format for expressing data in the RDF data model
content is always UTF-8. TriG RDF syntax extends Turtle with support for named graphs. N-Triples Notation3 (N3) LV2 "RDF 1.1 Turtle - Terse RDF Triple LanguageTurtle"
Turtle_(syntax)
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
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
regular graph, a distance-transitive graph, and a Ramanujan graph. Although its construction is folklore, it was named after Andries Brouwer and Willem H
Brouwer–Haemers_graph
Graph whose vertices correspond to combinations of a set of n elements
disjoint. Kneser graphs are named after Martin Kneser, who first investigated them in 1956. The Kneser graph K(n, 1) is the complete graph on n vertices
Kneser_graph
Graph representing edges of another graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges
Line_graph
Data query language developed by Facebook
or modified. A GraphQL server can process a client query using data from separate sources and present the results in a unified graph. The language is
GraphQL
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
Bipartite non-Hamiltonian polyhedral graph
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the
Herschel_graph
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
Cubic graph with 28 vertices and 42 edges
field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is
Coxeter_graph
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
Family of triangle-free circulant graphs
In graph theory, an Andrásfai graph is a triangle-free, circulant graph named after Béla Andrásfai. The Andrásfai graph And(n) for any natural number n
Andrásfai_graph
Type of knowledge base
knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used
Knowledge_graph
Cartesian product of complete graphs
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science
Hamming_graph
Two special graphs in graph theory
of genus 3, in which they form dual graphs. This is a 3-regular (cubic) graph with 56 vertices and 84 edges, named after Felix Klein. It is Hamiltonian
Klein_graphs
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Distance-regular graph with 56 vertices
The Gosset graph, named after Thorold Gosset, is a distance-regular graph with 56 vertices and valency 27. It is the 1-skeleton of the 7-dimensional 321
Gosset_graph
Distance-transitive cubic graph with 20 nodes and 30 edges
mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after Girard Desargues
Desargues_graph
the Ellingham–Horton 78-graph. They are named after Joseph D. Horton and Mark N. Ellingham, their discoverers. These two graphs provide counterexamples
Ellingham–Horton_graph
for the general theory, as well as Gallery of named graphs for a list with illustrations. R. Diestel, Graph Theory, p.8. 3rd Edition, Springer-Verlag, 2005
List of graphs by edges and vertices
List_of_graphs_by_edges_and_vertices
Bipartite 3-regular graph with 90 vertices and 135 edges
mathematical field of graph theory, the Foster graph is a bipartite 3-regular graph with 90 vertices and 135 edges. The Foster graph is Hamiltonian and has
Foster_graph
Class of undirected graphs defined from systems of sets
mathematics, Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J ( n , k ) {\displaystyle
Johnson_graph
Triangle-free graph requiring four colors
field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after
Grötzsch_graph
6-regular graph with 57 vertices and 171 edges
the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection
Perkel_graph
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
In graph theory, the Games graph is the largest known locally linear strongly regular graph. Its parameters as a strongly regular graph are (729,112,1
Games_graph
Graph whose embedding in a Euclidean space forms a regular tiling
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space R n {\displaystyle \mathbb {R}
Lattice_graph
Gewirtz graph is a strongly regular graph with 56 vertices and valency 10. It is named after the mathematician Allan Gewirtz, who described the graph in his
Gewirtz_graph
Non-crossing graph with vertices on outer face
In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar
Outerplanar_graph
Undirected bipartite graph with 112 vertices and 168 edges
field of graph theory, the Ljubljana graph is an undirected bipartite graph with 112 vertices and 168 edges, rediscovered in 2002 and named after Ljubljana
Ljubljana_graph
File format
DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename
DOT (graph description language)
DOT_(graph_description_language)
16-regular graph with 27 vertices and 216 edges
the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges
Schläfli_graph
Graph representing incident points and lines
we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line. They are named for Friedrich
Levi_graph
Planar bipartite graph with 25 vertices and 31 edges
mathematical field of graph theory, the Walther graph, also called the Tutte fragment, is a planar bipartite graph with 25 vertices and 31 edges named after Hansjoachim
Walther_graph
Graph with 15 vertices and 39 edges
In graph theory, the Poussin graph is a planar graph with 15 vertices and 39 edges. It is named after Charles Jean de la Vallée-Poussin. In 1879, Alfred
Poussin_graph
Graph with 30 vertices and 75 edges
the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. It
Meringer_graph
Graph with an antiprism as its skeleton
In the mathematical field of graph theory, an antiprism graph is a graph that has one of the antiprisms as its skeleton. An n-sided antiprism has 2n vertices
Antiprism_graph
edge-transitive graph which is not also symmetric. Such graphs are not common. It is named after Peter G. Doyle and Derek F. Holt, who discovered the same graph independently
Holt_graph
Assignment of labels to elements of a graph
discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally
Graph_labeling
In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian
Dyck_graph
Undirected unit-distance graph requiring four colors
In graph theory, a branch of mathematics, the Moser spindle (also called the Mosers' spindle or Moser graph) is an undirected graph, named after mathematicians
Moser_spindle
Graph with a triangular truncated trapezohedron as its skeleton
the mathematical field of graph theory, the Dürer graph is an undirected graph with 12 vertices and 18 edges. It is named after Albrecht Dürer, whose
Dürer_graph
Graph with 24 vertices and 36 edges
mathematical field of graph theory, the McGee graph or the (3-7)-cage is a 3-regular graph with 24 vertices and 36 edges. The McGee graph is the unique (3
McGee_graph
In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman
Laman_graph
Undirected unit-distance graph requiring four colors
In graph theory, the Golomb graph is a polyhedral graph with 10 vertices and 18 edges. It is named after Solomon W. Golomb, who constructed it (with a
Golomb_graph
Matrix representation of a graph
discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of
Laplacian_matrix
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Graph with sign-labeled edges
In the area of 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
Signed_graph
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
24-vertex symmetric bipartite cubic graph
mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David Eppstein after
Nauru_graph
Partition of a graph whose components are reachable from all vertices
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly
Strongly_connected_component
American software company
TigerGraph is a private company headquartered in Redwood City, California. It provides graph database and graph analytics software. TigerGraph was founded
TigerGraph
On forbidden subgraphs in planar graphs
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states
Kuratowski's_theorem
Graph with edges of length one, able to be drawn without crossings
In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line
Matchstick_graph
erroneous proof of the four color theorem; it was named after Errera by Hutchinson & Wagon (1998). The Errera graph is planar and has chromatic number 4, chromatic
Errera_graph
Graph whose biconnected components are all cliques
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component
Block_graph
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
Cubic graph with 8 vertices and 12 edges
mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder
Wagner_graph
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
Visualization of node-link graphs
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional
Graph_drawing
Infinite graph without small cliques
Henson graphs have the finite model property? More unsolved problems in mathematics In graph theory, the Henson graph Gi is an undirected infinite graph, the
Henson_graph
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Graph operation
In graph theory, a branch of mathematics, the Hajós construction is an operation on graphs named after György Hajós (1961) that may be used to construct
Hajós_construction
Graphs whose distances obey Ptolemy's inequality
In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek
Ptolemaic_graph
Bipartite, 3-regular undirected graph
field of graph theory, the Pappus graph is a bipartite, 3-regular, undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus
Pappus_graph
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic
Tutte_graph
Symmetric bipartite cubic graph with 16 vertices and 24 edges
mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand
Möbius–Kantor_graph
format for RDF (Resource Description Framework) graphs. It is a plain text format for serializing named graphs and RDF Datasets which offers a compact and
TriG_(syntax)
Undirected cubic graph with 12 vertices and 18 edges
the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich
Tietze's_graph
Planar graph with 23 vertices and 63 edges
edges. Its unique planar embedding has 42 triangular faces. The Kittell graph is named after Irving Kittell, who used it as a counterexample to Alfred Kempe's
Kittell_graph
Undirected graph named after S. S. Shrikhande
mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices
Shrikhande_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
Family of cubic graphs formed from regular and star polygons
In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding
Generalized_Petersen_graph
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 Jefferson Mason who coined the
Signal-flow_graph
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
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
In the mathematical field of graph theory, the Brinkmann graph is a 4-regular graph with 21 vertices and 42 edges discovered by Gunnar Brinkmann in 1992
Brinkmann_graph
Balanced complete multipartite graph
The Turán graph, denoted by T ( n , r ) {\displaystyle T(n,r)} , is a complete multipartite graph; it is formed by partitioning a set of n {\displaystyle
Turán_graph
Database for storage and retrieval of triples
a graph-based RDF model (such as mapping from SPARQL) onto SQL queries is difficult. Adding a name to the triple makes a "quad store" or named graph. A
Triplestore
Mathematical tree with cycle through leaves
In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four
Halin_graph
Cycle graph with all opposite nodes linked
vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M6 (the utility graph K3,3), Mn has exactly n/2 four-cycles which
Möbius_ladder
discipline of graph theory, the (m,n)-tadpole graph is a special type of graph consisting of a cycle graph on m (at least 3) vertices and a path graph on n vertices
Tadpole_graph
Measure of capacity of a communications channel defined from a graph
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 after
Shannon_capacity_of_a_graph
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