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Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Sequence of edges which join a sequence of vertices on a given graph
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct
Path_(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
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
Binary operation combining the vertex and edge sets of two graphs
In graph theory, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is analogous to the disjoint
Disjoint_union_of_graphs
Procedures for constructing new graphs in graph theory
In the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary (one input)
Graph_operations
In extremal graph theory, given a graph H {\displaystyle H} , a graph G {\displaystyle G} is said to be H {\displaystyle H} -saturated if G {\displaystyle
Saturation_(graph_theory)
Graph linking pairs of comparable elements in a partial order
In graph theory and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a
Comparability_graph
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
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Deleting a graph edge and merging its nodes
merging the two vertices that it previously joined. Edge contraction is a fundamental operation in the theory of graph minors. Vertex identification is a less
Edge_contraction
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_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)
Complete bipartite cut in a graph
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits
Split_(graph_theory)
Perfect graphs have neither odd holes nor odd antiholes
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither
Strong_perfect_graph_theorem
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first
Complete_bipartite_graph
Mathematical theory on behavior of connected clusters in a random graph
random graphs Fractal – Infinitely detailed mathematical structure Giant component – Large connected component of a random graph Graph theory – Area of
Percolation_theory
Graph family made by joining complete graphs at a universal node
field of graph theory, the windmill graph Wd(k,n) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at
Windmill_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
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
Theorem relating graph minors and topological embeddings
the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between the theory of
Graph_structure_theorem
Database using graph structures for queries
the decade, cloud-based graph databases such as Amazon Neptune and Neo4j AuraDB became available. Based on graph theory, graph databases store data in
Graph_database
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
Number of planar subgraphs to cover a graph
In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists
Thickness_(graph_theory)
American mathematician
specializing in graph theory. She is a professor of mathematics at Western Michigan University and the author of many textbooks on graph theory and mathematical
Ping_Zhang_(graph_theorist)
American mathematician
areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree
Fan_Chung
term geometric graph is sometimes used in a broader, somewhat vague sense.) The theory of topological graphs is an area of graph theory, mainly concerned
Topological_graph
Planar graph with 5 nodes and 6 edges
mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices
Butterfly_graph
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types
List_of_graphs
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
British-Canadian codebreaker and mathematician (1917–2002)
of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable importance. At a time when graph theory was
W._T._Tutte
Graph coloring where graph elements are assigned sets of colors
in a branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each
Fractional_coloring
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
Embedding of the circle in three dimensional Euclidean space
of 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)
Graph modeling collaboration in a social network
participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure
Collaboration_graph
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
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
Concept in order theory
In mathematics, specifically order theory, the join of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the supremum (least
Join_and_meet
Mapping of a graph into a tree
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain
Tree_decomposition
Finding shortest walks through all graph edges
In graph theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find
Chinese_postman_problem
Theory of attitude change
colloquium on balance theory, Bo Anderson struck at the heart of the notion: In graph theory there exists a formal balance theory that contains theorems
Balance_theory
Intersection graph of trapezoids between parallel lines
In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that
Trapezoid_graph
Flow graph invented by Claude Shannon
signal-flow graph theory builds on that of directed graphs (also called digraphs), which includes as well that of oriented graphs. This mathematical theory of
Signal-flow_graph
Mathematical problem
are the same color? More unsolved problems in mathematics In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson
Hadwiger–Nelson_problem
Planar maps require at most four colors
terms of graph theory, by considering it in terms of constructing a graph coloring of the planar graph of adjacencies between regions. In graph-theoretic
Four_color_theorem
Set whose pairs have minima and maxima
analysis and Lattice Miner (theory and tool) Bloom filter Information flow Ordinal optimization Quantum logic Median graph Knowledge space Regular language
Lattice_(order)
Smallest transitive relation containing a given binary relation
and transitive reduction are also used in the closely related area of graph theory. A relation R on a set X is transitive if, for all x, y, z in X, whenever
Transitive_closure
7-regular undirected graph with 50 nodes and 175 edges
of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with
Hoffman–Singleton_graph
In graph theory, a graph amalgamation is a relationship between two graphs (one graph is an amalgamation of another). Similar relationships include subgraphs
Graph_amalgamation
In graph theory, edges incident/directed between the same vertices
In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same
Multiple_edges
In graph theory, a fan graph (also called a path-fan graph) is a graph formed by the join of a path graph and an empty graph on a single vertex. The fan
Fan_graph
On coloring the edges of graphs
In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than
Vizing's_theorem
Characterization of graphs with perfect matchings
mathematical discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings
Tutte's theorem on perfect matchings
Tutte's_theorem_on_perfect_matchings
2003 mathematics text
Elementary Number Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible to
Elementary Number Theory, Group Theory and Ramanujan Graphs
Elementary_Number_Theory,_Group_Theory_and_Ramanujan_Graphs
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
Independent set which is not a subset of any other independent set
In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. In other
Maximal_independent_set
Mathematical tree of cycles
In graph theory, a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently
Cactus_graph
Branch of mathematics
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing
Order_theory
Constructs with triply-connected vertices
(1977). "A canonical representation of trivalent Hamiltonian graphs". Journal of Graph Theory. 1 (1): 45–60. doi:10.1002/jgt.3190010111. MR 0463029. Clark
Table_of_simple_cubic_graphs
the graph-theoretic analogue of the topological rose, a space of m {\displaystyle m} circles joined at a point. When the context of graph theory is clear
Bouquet_graph
W. (1978). "10. Line Graphs and Line Digraphs". In Beineke, Lowell W.; Wilson, Robin J. (eds.). Selected Topics in Graph Theory. Academic Press. p. 277
Skein_(graph_theory)
number 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
Graph formed by adding isolated or universal vertices
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Threshold_graph
Three raised to an integer power
system. In graph theory, powers of three appear in the Moon–Moser bound 3n/3 on the number of maximal independent sets of an n-vertex graph, and in the
Power_of_three
Unsolved problem on graph coloring
the graph. Therefore, biplanar graphs require at most 12 colors. An example of a biplanar graph requiring 9 colors can be constructed as the join of a
Earth–Moon_problem
Database class for storage and retrieval of modeled data
queries involving joins or non-indexed filtering varies depending on the database type—document, key–value, wide-column, or graph—and the specific implementation
NoSQL
Overview of and topical guide to algorithms
matching Hopcroft–Karp algorithm Blossom algorithm Graph coloring Clique problem Independent set (graph theory) Hamiltonian path problem Travelling salesman
Outline_of_algorithms
On chains and antichains in partial orders
In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of
Dilworth's_theorem
Hungarian mathematician
a Hungarian mathematician whose research concerns combinatorics and graph theory. Szegedy earned a master's degree in 1998 and a PhD in 2003 from Eötvös
Balázs_Szegedy
Characterizes the height of any finite partially ordered set
7. Coloring and other problems on comparability graphs", Algorithmic Graph Theory and Perfect Graphs, New York: Academic Press, pp. 132–135, ISBN 0-12-289260-7
Mirsky's_theorem
Visual depiction of a partially ordered set
Ivan (1985), "The diagram", in Rival, Ivan (ed.), Graphs and Order: The Role of Graphs in the Theory of Ordered Sets and Its Applications, Proceedings
Hasse_diagram
Planar graphs have straight drawings
In the mathematical field of graph theory, Fáry's theorem states that any simple, planar graph can be drawn without crossings so that its edges are straight
Fáry's_theorem
Abstraction of linear independence of vectors
to a geometric lattice. Matroid theory borrows extensively from the terms used in both linear algebra and graph theory, largely because it is the abstraction
Matroid
Network whose degree distribution follows a power law
; Tanaka, R.; Doyle, J.C.; Willinger, W. (2005). "Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)"
Scale-free_network
Planar maps require at most five colors
The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world,
Five_color_theorem
Type of dominating set in graph theory
In graph theory, a Roman dominating set (RDS) is a special type of dominating set inspired by historical military defense strategies of the Roman Empire
Roman_dominating_set
constraint satisfaction problems. In graph theory, a separating vertex is a node of a graph that "breaks" the graph when removed from it. Formally, it is
Decomposition method (constraint satisfaction)
Decomposition_method_(constraint_satisfaction)
Measure of graph complexity
In graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth
Clique-width
Graph which partitions into a clique and independent set
In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split
Split_graph
Form taken by the network of interconnections of a circuit
of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can
Circuit_topology_(electrical)
Directed graph which is also a multigraph
mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between
Quiver_(mathematics)
American computer scientist and educator
design and analysis of algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational biology
Satish_B._Rao
Computer scientist
scientist known for his work in algorithms, game theory, social networks, network design, graph theory, and big data. He has over 200 publications with
Mohammad_Hajiaghayi
Positive-definite integral set of repeated points with Abelian group-rank 24
isomorphic.) The Kneser neighborhood graph in 8n dimensions has a point for each even lattice, and a line joining two points for each odd 8n dimensional
Niemeier_lattice
Graph with directed and undirected edges
In graph theory, a mixed graph G = (V, E, A) is a graph consisting of a set of vertices V, a set of (undirected) edges E, and a set of directed edges (or
Mixed_graph
Binary relation over a set and itself
types of endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations
Homogeneous_relation
Mathematical ways to group elements of a set
or a partition is sometimes called a setoid, typically in type theory and proof theory. A partition of a set X is a set of non-empty subsets of X such
Partition_of_a_set
covering graph over a finite graph ), and is closely related to that of a Tessellation of space (or honeycomb) in the theory of polytopes and similar areas
Periodic graph (crystallography)
Periodic_graph_(crystallography)
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges
Forbidden_subgraph_problem
Hungarian mathematician (born 1965)
mathematician working in graph theory and combinatorics. He is a professor and head of the Department of Computer Science and Information Theory at the Budapest
Gyula_Y._Katona
American mathematician (1921–2005)
mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition
Frank_Harary
German mathematician, specialist in combinatorics
second edition Design Theory (1999) was split into two volumes, one and two. In 1990 Jungnickel wrote an article on geometric and graph-theoretical aspects
Dieter_Jungnickel
Hungarian mathematician (1884–1944)
field of graph theory. Kőnig was born in Budapest, the son of mathematician Gyula Kőnig. In 1907, he received his doctorate at, and joined the faculty
Dénes_Kőnig
Solid with six equal square faces
drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube
Cube
Natural number
Combinatorial Matrix Theory to Laplacian Matrices of Graphs. CRC Press. p. 197. ISBN 978-1-4398-6339-8. ... The complete graph on the largest number
4
Mathematician at Courant Institute of Mathematical Sciences
Mathematical Sciences at New York University working in combinatorics and graph theory. She and Huy Tuan Pham proved the Kahn–Kalai conjecture on estimating
Jinyoung_Park_(mathematician)
British mathematician (1916–2020)
He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory. He is best known for co-authorship (with
Richard_K._Guy
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JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Hebrew, Japanese, Norwegian, Swedish, Swiss, Ukrainian
The Lord is Gracious; God has Given; Gift of God; God is Gracious; Jehovah has been Gracious; Variant of John; Abbreviation of Jonathan
Girl/Female
American, Australian, British, Chinese, Christian, English, Hebrew
Modern Female Version of John and Jon; The Lord is Gracious
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Hindu
God has been gracious: has shown favor in the bible John the baptist baptized christ in the jordan
Male
Finnish
Finnish form of Greek Ioannes (Latin Johannes), JONI means "God is gracious."
Female
English
Variant spelling of English Jonie, JONI means "God is gracious."
Female
English
Variant spelling of English Joy, JOI means "joy."
Boy/Male
Irish
Form of John the Baptist.
Male
English
 Anglicized form of Greek Ioannes (Latin Johannes), JOHN means "God is gracious." In the bible, this is the name of many characters, including John the Baptist.
Boy/Male
Muslim
Grape
Female
English
Medieval English contracted form of Old French Johanne, JOAN means "God is gracious." Compare with masculine Joan.
Male
Irish
Irish Gaelic form of Greek Ioannes, EOIN means "God is gracious."
Male
English
 Pet form of English Jonathan, JON means "God has given." Compare with other forms of Jon.
Female/Male/Unisex
Korean
(豪金) Korean name JIN-HO means "golden hero/leader."
Boy/Male
Arabic, Modern
Grape
Boy/Male
American, British, English, French, Greek, Hebrew
God is Gracious; Jehovah has been Gracious; Variant of John or Abbreviation of Jonathan Jehovah has been Gracious; Has Shown Favor
Surname or Lastname
English, Welsh, German, etc.
English, Welsh, German, etc. : ultimately from the Hebrew personal name yÅÌ£hÄnÄn ‘Jehovah has favored (me with a son)’ or ‘may Jehovah favor (this child)’. This personal name was adopted into Latin (via Greek) as Johannes, and has enjoyed enormous popularity in Europe throughout the Christian era, being given in honor of St. John the Baptist, precursor of Christ, and of St. John the Evangelist, author of the fourth gospel, as well as others of the nearly one thousand other Christian saints of the name. Some of the principal forms of the personal name in other European languages are Welsh Ieuan, Evan, Siôn, and Ioan; Scottish Ia(i)n; Irish Séan; German Johann, Johannes, Hans; Dutch Jan; French Jean; Italian Giovanni, Gianni, Ianni; Spanish Juan; Portuguese João; Greek IÅannÄ“s (vernacular Yannis); Czech Jan; Russian Ivan. Polish has surnames both from the western Slavic form Jan and from the eastern Slavic form Iwan. There were a number of different forms of the name in Middle English, including Jan(e), a male name (see Jane); Jen (see Jenkin); Jon(e) (see Jones); and Han(n) (see Hann). There were also various Middle English feminine versions of this name (e.g. Joan, Jehan), and some of these were indistinguishable from masculine forms. The distinction on grounds of gender between John and Joan was not firmly established in English until the 17th century. It was even later that Jean and Jane were specialized as specifically feminine names in English; bearers of these surnames and their derivatives are more likely to derive them from a male ancestor than a female. As a surname in the British Isles, John is particularly frequent in Wales, where it is a late formation representing Welsh Siôn rather than the older form Ieuan (which gave rise to the surname Evan). As an American family name this form has absorbed various cognates from continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
Indian
Grape
Girl/Female
English American
Modern feminine of John and Jon.
Male
Scandinavian
 Scandinavian form of Icelandic Jóhann, JON means "God is gracious." Compare with other forms of Jon.
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
JOIN GRAPH-THEORY
v. t.
To separate the joints; of; to divide at the joint or joints; to disjoint; to cut up into joints, as meat.
n.
A joining of two things or parts so as to admit of motion; an articulation, whether movable or not; a hinge; as, the knee joint; a node or joint of a stem; a ball and socket joint. See Articulation.
v. i.
To fit as if by joints; to coalesce as joints do; as, the stones joint, neatly.
a.
Joined; united; combined; concerted; as joint action.
v. t.
To associate one's self to; to be or become connected with; to league one's self with; to unite with; as, to join a party; to join the church.
v. t.
To make or fabricate; to invent; to originate; as, to coin a word.
v. t.
To provide with a joint or joints; to articulate.
v. i.
To be contiguous, close, or in contact; to come together; to unite; to mingle; to form a union; as, the hones of the skull join; two rivers join.
a.
Shared by, or affecting two or more; held in common; as, joint property; a joint bond.
n.
The space between the adjacent surfaces of two bodies joined and held together, as by means of cement, mortar, etc.; as, a thin joint.
v. t.
To unite by a joint or joints; to fit together; to prepare so as to fit together; as, to joint boards.
v. t.
To make of a definite fineness, and convert into coins, as a mass of metal; to mint; to manufacture; as, to coin silver dollars; to coin a medal.
n.
The place or part where two things or parts are joined or united; the union of two or more smooth or even surfaces admitting of a close-fitting or junction; junction as, a joint between two pieces of timber; a joint in a pipe.
n.
The part or space included between two joints, knots, nodes, or articulations; as, a joint of cane or of a grass stem; a joint of the leg.
v. t.
To accept, or engage in, as a contest; as, to join encounter, battle, issue.
v. t.
To join; to connect; to unite; to combine.
a.
United, joined, or sharing with another or with others; not solitary in interest or action; holding in common with an associate, or with associates; acting together; as, joint heir; joint creditor; joint debtor, etc.
p. pr. & vb. n.
of Join
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