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Graph with a total order over its nodes
An ordered graph is a graph with a total order over its nodes. In an ordered graph, the parents of a node are the nodes that are adjacent to it and precede
Ordered_graph
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 with no directed cycles
directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering
Directed_acyclic_graph
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)
In graph theory, the interval chromatic number χ < ( H ) {\displaystyle \chi _{<}(H)} of an ordered graph H {\displaystyle H} is the minimum number of
Interval_coloring
Abstract data type in computer science
undirected graph or a set of ordered pairs for a directed graph. These pairs are known as edges (also called links or lines), and for a directed graph are also
Graph_(abstract_data_type)
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
Data storage paradigm in computing
RocksDB. Some NewSQL databases are supported by ordered key–value stores. JanusGraph, a property graph database, has both a Berkeley DB backend and FoundationDB
Ordered_key–value_store
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 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 with oriented edges
a directed graph is an ordered pair G = (V, A) where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices
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
Fundamental unit of which graphs are formed
vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented
Vertex_(graph_theory)
Mathematical set with an ordering
directed acyclic graph ordered by reachability. The set of subspaces of a vector space ordered by inclusion. For a partially ordered set P, the sequence
Partially_ordered_set
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
On chains and antichains in partial orders
combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain of incomparable elements equals the
Dilworth's_theorem
Adjacent subset of an undirected graph
In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are
Clique_(graph_theory)
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
OGDL (Ordered Graph Data Language), is a "structured textual format that represents information in the form of graphs, where the nodes are strings and
OGDL
Characterizes the height of any finite partially ordered set
directed acyclic graphs (representing a partially ordered set by reachability of their vertices), as the statement that there exists a graph homomorphism
Mirsky's_theorem
Visual depiction of a partially ordered set
the directed acyclic graph obtained from the covering relation of a partially ordered set, independently of any drawing of that graph. Although Hasse diagrams
Hasse_diagram
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
Partition of vertices of a directed graph
In graph theory, the weak components of a directed graph partition the vertices of the graph into subsets that are totally ordered by reachability. They
Weak_component
Graph linking pairs of comparable elements in a partial order
partially ordered set, take the directed acyclic graph, apply transitive closure, and remove orientation. Equivalently, a comparability graph is a graph that
Comparability_graph
Algebraic object with an ordered structure
orderings. Every subfield of an ordered field is also an ordered field in the inherited order. Every ordered field contains an ordered subfield that is isomorphic
Ordered_field
Order-zero graph or any edgeless graph
graph is useful depends on context. On the positive side, K0 follows naturally from the usual set-theoretic definitions of a graph (it is the ordered
Null_graph
Graph of intervisible locations in computational geometry
between them in the graph. When the set of locations lies in a line, this can be understood as an ordered series. Visibility graphs have therefore been
Visibility_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
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
Finiteness of sets of forbidden graph minors
graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor
Robertson–Seymour_theorem
On coloring infinite graphs
extending the four-color theorem and Dilworth's theorem from finite graphs and partially ordered sets to infinite ones, and reducing the Hadwiger–Nelson problem
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
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
Assignment of labels to elements of a graph
graph is called an edge-labeled graph. When the edge labels are members of an ordered set (e.g., the real numbers), it may be called a weighted graph
Graph_labeling
Data organization and storage formats
(example Priority queue) Double-ended queue Graph (example Tree, Heap) Some properties of abstract data types: "Ordered" means that the elements of the data
List_of_data_structures
Concept in graph theory
equals e {\displaystyle e} or f {\displaystyle f} . A graph can be formally defined as an ordered triple ( V , E , ψ ) {\displaystyle (V,E,\psi )} , where
Incidence_(graph)
Cartesian product of complete graphs
q elements and d a positive integer. The Hamming graph H(d,q) has vertex set Sd, the set of ordered d-tuples of elements of S, or sequences of length
Hamming_graph
Order whose elements are all comparable
example is the use of "chain" as a synonym for a walk in a graph. One may define a totally ordered set as a particular kind of lattice, namely one in which
Total_order
Flow chart in business processing
event-driven process chains: An Event-driven process chain (EPC) is an ordered graph of events and functions. It provides various connectors that allow alternative
Event-driven_process_chain
Generalized alphabetical order
order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations
Lexicographic_order
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 representing a permutation
In the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent
Permutation_graph
relationship in directed trees and directed series–parallel graphs. The comparability graphs of series-parallel partial orders are cographs. Series-parallel
Series-parallel_partial_order
Linked node hierarchical data structure
the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with
Tree_(abstract_data_type)
Regular graph used in coding theory
A trellis is a graph whose nodes are ordered into vertical slices (time) with every node at almost every time connected to at least one node at an earlier
Trellis_(graph)
Complements of perfect graphs are perfect
In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph
Perfect_graph_theorem
Intersection graph for intervals on the real number line
intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring
Interval_graph
Database class for storage and retrieval of modeled data
databases use a single data structure—such as key–value pairs, wide columns, graphs, or documents—to hold information. Since this non-relational design does
NoSQL
Numerical invariant of graphs
ranking number, ordered chromatic number, and minimum elimination tree height; it is also closely related to the cycle rank of directed graphs and the star
Tree-depth
Tree which includes all vertices of a graph
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may
Spanning_tree
Graph with multiple edges between two vertices
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges)
Multigraph
Planar directed acyclic graph
In graph theory, an st-planar graph is a bipolar orientation of a plane graph for which both the source and the sink of the orientation are on the outer
St-planar_graph
Graph with same nodes as but complementary connections to another
directed graph and let O consist of all ordered pairs of distinct vertices in V. Then the simple directed graph H = (V, O \ A) is the complement of G.
Complement_graph
German World War II submarine
HMS Graph (pennant number P715) was a German Type VIIC U-boat captured and recommissioned by the British Royal Navy during World War II. Commissioned
HMS_Graph
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)
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
Association of one output to each input
three sets (often as an ordered triple), the domain X , {\displaystyle X,} the codomain Y , {\displaystyle Y,} and the graph R {\displaystyle R} that
Function_(mathematics)
Order-preserving mathematical function
mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose
Monotonic_function
Branch of discrete mathematics
concepts and methods in topology are used to study graph coloring, fair division, partitions, partially ordered sets, decision trees, necklace problems and discrete
Combinatorics
Type of graph in graph theory
ordered pairs of linked vertices. Every connected symmetric graph must be vertex-transitive and edge-transitive, and the converse is true for graphs of
Half-transitive_graph
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter
Geometric_graph_theory
twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively
Twin-width
In graph theory, the shift graph Gn,k for n , k ∈ N , n > 2 k > 0 {\displaystyle n,k\in \mathbb {N} ,\ n>2k>0} is the graph whose vertices correspond
Shift_graph
Graph with a median for each three vertices
them "median graphs" appears to be Nebeský (1971). As Chung, Graham, and Saks write, "median graphs arise naturally in the study of ordered sets and discrete
Median_graph
Edge-face adjacencies in another graph
graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were
Medial_graph
Geometric model of the planar projection of the physical universe
Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to
Euclidean_plane
Fast-growing function
is a graph minor of) G j {\displaystyle G_{j}} . The Robertson–Seymour theorem proves that subcubic graphs (simple or not) are well-quasi-ordered by homeomorphic
Friedman's_SSCG_function
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
Well-quasi-ordering of finite trees
transfinite recursion). In 2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important
Kruskal's_tree_theorem
Horizontal and vertical axes/coordinate numbers of a 2D coordinate system or graph
{\displaystyle \equiv y} -axis (vertical) coordinate Together they form an ordered pair which defines the location of a point in two-dimensional rectangular
Abscissa_and_ordinate
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
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
Intersection graph of unit intervals on the real line
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting
Indifference_graph
the variables that makes the ordered graph of constraint having width 1. Such an ordering exists if and only if the graph of constraints is a tree. If
Local_consistency
Graphical representation of data
A chart (sometimes known as a graph) is a graphical representation for data and information visualization, in which "the data is represented by symbols
Chart
Type of chart
A line chart or line graph, also known as curve chart, is a type of chart that displays information as a series of data points called 'markers' connected
Line_chart
Index of articles associated with the same name
undirected graphs Elimination ordering of chordal graphs Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)
Order_(mathematics)
General concept and operation in mathematics
polyhedron, one can form a planar graph, the graph of its vertices and edges. The dual polyhedron has a dual graph, a graph with one vertex for each face
Duality_(mathematics)
combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Concept in graph theory
In graph theory, a bound graph expresses which pairs of elements of some partially ordered set have an upper bound. Rigorously, any graph G is a bound
Bound_graph
Hierarchical clustering of graph edges
In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree
Branch-decomposition
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
Type of graph in mathematics
In graph theory, a branch of mathematics, a half graph is a special type of bipartite graph. These graphs are called the half graphs because they have
Half_graph
Diagram of behavior of finite state systems
classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q0, F): Vertices Q: a finite set
State_diagram
Property of elements related by inequalities
{\displaystyle x,} and likewise for incomparability. The comparability graph of a partially ordered set P {\displaystyle P} has as vertices the elements of P {\displaystyle
Comparability
Data structure for Boolean functions
sharing to several BDDs, i.e. one sub-graph is used by several BDDs, the data structure Shared Reduced Ordered Binary Decision Diagram is defined. The
Binary_decision_diagram
Special case of the perfect graphs in graph theory
In graph theory, a perfectly orderable graph is a graph whose vertices can be ordered in such a way that a greedy coloring algorithm with that ordering
Perfectly_orderable_graph
Intersection graph of trapezoids between parallel lines
partially ordered set, P = (X, <), is the minimum number d of interval orders P1 … Pd such that P = P1 ∩ … ∩ Pd. The incomparability graph of a partially
Trapezoid_graph
Smallest transitive relation containing a given binary relation
closure 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,
Transitive_closure
Mathematical proposition equivalent to the axiom of choice
theory. It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset) necessarily contains at least
Zorn's_lemma
Finite ordered list of elements
sets of ordered pairs Functions are commonly identified with their graphs, which is a certain set of ordered pairs. Indeed, many authors use graphs as the
Tuple
An object whose endomorphisms are isomorphic to another structure
of spectral graph theory. Dual to the observation above that every graph is an intersection graph is the fact that every partially ordered set (also known
Representation_(mathematics)
Periodic spatial graph
Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three
Laves_graph
Vector space with a partial order
In mathematics, an ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with
Ordered_vector_space
Mathematical measure for partial orders
partially ordered set has order dimension at most two, for instance, by testing whether the comparability graph of the partial order is a permutation graph. However
Order_dimension
Directed graph where each vertex pair has one arc
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently
Tournament_(graph_theory)
Term in the mathematical area of order theory
mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This
Duality_(order_theory)
Abstract simplicial complex describing a graph's cliques
mathematical objects in graph theory and geometric topology that each describe the cliques (complete subgraphs) of an undirected graph. The clique complex
Clique_complex
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
One-by-one assignment of colors to graph vertices
of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a graph formed
Greedy_coloring
Study of discrete mathematical structures
Order theory is the study of partially ordered sets, both finite and infinite. Graph theory, the study of graphs and networks, is often considered part
Discrete_mathematics
travel, tourism, insurance
ORDERED GRAPH
ORDERED GRAPH
Male
English
Old English Arthurian legend name of a Knight of the Round Table who was the illegitimate son and traitor of King Arthur, possibly MORDRED means "sea counsel." He was brother (or half-brother) to Agravain, Gaheris, Gareth, and Gawain, and noted for having crowned himself and married Guinevere while Arthur was waging war on Emperor Lucius of Rome. He was killed by Arthur at the Battle of Camlann.Â
Boy/Male
English Arthurian Legend
Brave.
Boy/Male
Muslim
Ordered, Pasted, Appointed
Boy/Male
Indian
Ordered, Pasted, Appointed
Girl/Female
Indian
Well-arranged, Well-ordered
Girl/Female
Shakespearean
The Tragedy of Macbeth' Lady Macduff, wife to Macduff, murdered on Macbeth's orders.
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place in Lancashire, called Ormerod, from the Old Norse personal name Ormr (see Orme 1) or Ormarr (a compound of orm ‘serpent’ + herr ‘army’) + Old English rod ‘clearing’.
Male
Arthurian
, a son of Lot; traitor to Arthur.
Boy/Male
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Boy/Male
Hindu
Orderly
Girl/Female
English, Peruvian
Plaster; Powdered
Boy/Male
Indian
Responsibility; Ordered
Girl/Female
Muslim
Well-arranged, Well-ordered
Girl/Female
Greek
Murdered Agamemnon.
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
Mitanshu | மீதாஂஷà¯Â
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Boy/Male
Tamil
Orderly
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
ORDERED GRAPH
ORDERED GRAPH
ORDERED GRAPH
ORDERED GRAPH
ORDERED GRAPH
ORDERED GRAPH
ORDERED GRAPH
a.
Performed in good or established order; well-regulated.
a.
Having three corners, or angles; as, a three-cornered hat.
a.
Observant of order, authority, or rule; hence, obedient; quiet; peaceable; not unruly; as, orderly children; an orderly community.
n.
One who puts in order, arranges, methodizes, or regulates.
n.
To give an order to; to command; as, to order troops to advance.
n.
A noncommissioned officer or soldier who attends a superior officer to carry his orders, or to render other service.
n.
An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry.
a.
Covered or adorned with osiers; as, osiered banks.
a.
Having three prominent longitudinal angles; as, a three-cornered stem.
imp. & p. p.
of Order
a.
Being on duty; keeping order; conveying orders.
adv.
According to due order; regularly; methodically; duly.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
a.
Conformed to order; in order; regular; as, an orderly course or plan.
v. i.
To give orders; to issue commands.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
n.
One who gives orders.
a.
Well-ordered; orderly; regular; methodical.
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