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Graph in which every two vertices are adjacent
of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph
Complete_graph
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
Geometric graph with unit edge lengths
complete graph on two vertices is a unit distance graph, as is the complete graph on three vertices (the triangle graph), but not the complete graph on
Unit_distance_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
Adjacent subset of an undirected graph
clique of a graph G {\displaystyle G} is an induced subgraph of G {\displaystyle G} that is complete. Cliques are one of the basic concepts of graph theory
Clique_(graph_theory)
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
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
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
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 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
Subgraph with contracted edges
of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the complete bipartite
Graph_minor
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)
Abstract regular polyhedron with 10 triangular faces
{\displaystyle K_{6}} (the complete graph with 6 vertices) on a real projective plane. With this embedding, the dual graph is the Petersen graph --- see hemi-dodecahedron
Hemi-icosahedron
Unsolved problem in computational complexity theory
determining whether two finite graphs are isomorphic. The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in
Graph_isomorphism_problem
Graph made from disjoint union of complete graphs
In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs. Equivalently, a graph is a cluster
Cluster_graph
Cubic graph with 10 vertices and 15 edges
Petersen graph is nonplanar. Any nonplanar graph has as minors either the complete graph K5, or the complete bipartite graph K3,3, but the Petersen graph has
Petersen_graph
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
Graph with nodes connected in a closed chain
related to Cycle graphs. Complete bipartite graph Complete graph Circulant graph Cycle graph (algebra) Null graph Path graph Some simple graph spectra. win
Cycle_graph
Path in a graph that visits each vertex exactly once
problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details. Hamiltonian paths and
Hamiltonian_path
Directed graph where each vertex pair has one arc
orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in both directions
Tournament_(graph_theory)
Basic concept of graph theory
mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that
Connectivity_(graph_theory)
Fewest edge crossings in drawing of a graph
graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is
Crossing number (graph theory)
Crossing_number_(graph_theory)
Graph of chess rook moves
graphs through their alternative constructions: rook's graphs are the Cartesian product of two complete graphs, and are the line graphs of complete bipartite
Rook's_graph
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 a graph into spanning subgraphs
If the complete graph Kn+1 has a perfect 1-factorization, then the complete bipartite graph Kn,n also has a perfect 1-factorization. If a graph is 2-factorable
Graph_factorization
Topics referred to by the same term
an ideal Completeness (cryptography) Completeness (statistics), a statistic that does not allow an unbiased estimator of zero Complete graph, an undirected
Completeness
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
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
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Concept in graph theory
regular graphs. These include the disjoint union of one or more equal-sized complete graphs, and their complements, the complete multipartite graphs with
Strongly_regular_graph
the complete graph K4 (such a characterisation is known for K4-free planar graphs) Classify graphs with representation number 3, that is, graphs that
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
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
Star polygon with 12 vertices
degenerate compound of six digons (line segments), {12/6} – produces the complete graph K12. Dodecagrams can also be incorporated into uniform polyhedra. Below
Dodecagram
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
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)
Describing a family of graphs by excluding certain (sub)graphs
graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph K5
Forbidden graph characterization
Forbidden_graph_characterization
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Graph whose vertices correspond to combinations of a set of n elements
Kneser graph K(n, 2) is the complement of the line graph of the complete graph on n vertices. The Kneser graph K(2n − 1, n − 1) is the odd graph On; in
Kneser_graph
Toroidal polyhedron with 14 triangle faces
vertices and 21 edges of the Császár polyhedron form an embedding of the complete graph K7 onto a topological torus. Of the 35 possible triangles from vertices
Császár_polyhedron
Trail in a graph that visits each edge once
first complete proof of this latter claim was published posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has
Eulerian_path
Unproven generalization of the four-color theorem
in mathematics Does every graph with chromatic number k {\displaystyle k} have a k {\displaystyle k} -vertex complete graph as a minor? More unsolved
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
Number of edges touching a vertex in a graph
degree is 0. In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph (denoted K n {\displaystyle
Degree_(graph_theory)
Type of graph
biconnected graph has no articulation vertices. The property of being 2-connected is equivalent to biconnectivity, except that the complete graph of two vertices
Biconnected_graph
two-graph on the set E. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs. Switching
Two-graph
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
8-vertex complete graph K8. The vertices of the Gosset graph can be identified with two copies of the set of edges of K8. Two vertices of the Gosset graph that
Gosset_graph
Bijection between the vertex set of two graphs
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to
Graph_isomorphism
Graph able to be partitioned into multiple independent sets
applied to the resources. Example complete k-partite graphs A complete k-partite graph is a k-partite graph in which there is an edge between every pair of
Multipartite_graph
Cartesian product of complete graphs
which is the complete graph Kq H(2,q), which is the lattice graph Lq,q and also the rook's graph H(d,1), which is the singleton graph K1 H(d,2), which
Hamming_graph
Graph linking pairs of comparable elements in a partial order
graphs are a subclass of string graphs; the complement of every comparability graph is a string graph. Every complete graph is a comparability graph,
Comparability_graph
Type of graph in mathematical graph theory
discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices
Lollipop_graph
Graph with at most one crossing per edge
color these graphs, in the worst case, was shown to be six. The example of the complete graph K6, which is 1-planar, shows that 1-planar graphs may sometimes
1-planar_graph
Binary operation combining the vertex and edge sets of two graphs
cluster graphs are the disjoint unions of complete graphs. The 2-regular graphs are the disjoint unions of cycle graphs. More generally, every graph is the
Disjoint_union_of_graphs
Graph with same nodes as but complementary connections to another
graph H = (V, O \ A) is the complement of G. Let G be a simple undirected / directed graph, let K be the complete simple undirected / directed graph on
Complement_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
Graphs that differ only by edge subdivision
In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G
Homeomorphism_(graph_theory)
Polynomial in combinatorial mathematics
3a_{1}a_{2}+2a_{3}\right).} It happens that the complete graph K3 is isomorphic to its own line graph (vertex-edge dual) and hence the edge permutation
Cycle_index
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Order-zero graph or any edgeless graph
mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes
Null_graph
Undirected graph
In graph theory, a critical graph is an undirected graph all of whose proper subgraphs have smaller chromatic number. In such a graph, every vertex or
Critical_graph
Graph able to be embedded on a torus
Heawood graph, the complete graph K7 (and hence K5 and K6), the Petersen graph (and hence the complete bipartite graph K3,3, since the Petersen graph contains
Toroidal_graph
Graph whose embedding in a Euclidean space forms a regular tiling
number of complete graphs. A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the graph whose vertices
Lattice_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
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 representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Mathematical function
one of selecting a perfect matching in a complete graph with two fewer vertices. For instance, a complete graph with four vertices a, b, c, and d has three
Double_factorial
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)
Assigning directions to the edges of an undirected graph
graph can be converted to an oriented graph by removing every 2-cycle, and conversely an oriented graph can be converted to a complete directed graph
Orientation_(graph_theory)
Least-weight tree connecting graph vertices
tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the
Minimum_spanning_tree
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
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
Mathematical game played on a graph
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling
Graph_pebbling
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
Linear algebra aspects of graph theory
labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined
Spectral_graph_theory
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)
Class of undirected graphs defined from systems of sets
) {\displaystyle J(n,n-1)} are the complete graph Kn. J ( 4 , 2 ) {\displaystyle J(4,2)} is the octahedral graph. J ( 5 , 2 ) {\displaystyle J(5,2)}
Johnson_graph
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
Paley graph is a circulant graph. Every Möbius ladder is a circulant graph, as is every complete graph. A complete bipartite graph is a circulant graph if
Circulant_graph
Natural number
are not, in general, sufficient to guarantee this. The largest planar complete graph has four vertices. A solid figure with four faces as well as four vertices
4
_{2}n} bipartite graphs. Proof By monotonicity, no bipartite graph can have graph entropy greater than that of a complete bipartite graph, which is bounded
Graph_entropy
On complete subdivisions in nonplanar graphs
in 2020. A graph is 5-vertex-connected when there are no five vertices that removed leave a disconnected graph. The complete graph is a graph with an edge
Kelmans–Seymour_conjecture
Graph with almost the max amount of edges
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected
Dense_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
Task in computational graph theory
a graph is an example of a complete graph invariant: every two isomorphic graphs have the same canonical form, and every two non-isomorphic graphs have
Graph_canonization
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
Integer associated with a graph
distance graph to more than 2 dimensions. In the worst case, every pair of vertices is connected, giving a complete graph. To immerse the complete graph K n
Dimension_(graph_theory)
Graph of zero divisors of a commutative ring
zero-divisor graph of the ring of integers modulo n {\displaystyle n} (with only the zero divisors as its vertices) is either a complete graph or a complete bipartite
Zero-divisor_graph
Number of spanning trees of a complete graph
n^{n-2}} . The formula equivalently counts the spanning trees of a complete graph with labeled vertices (sequence A000272 in the OEIS). Many proofs of
Cayley's_formula
Number of vertices with unambiguous distances
dimension of a graph is an NP-hard problem; the decision version, determining whether the metric dimension is less than a given value, is NP-complete. For an
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Mathematical ways to group elements of a set
the edges of a complete graph. The matroid closure of a set of atomic partitions is the finest common coarsening of them all; in graph-theoretic terms
Partition_of_a_set
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
Family of graphs with 2n nodes and n(n-1) edges
with an edge from ui to vj whenever i ≠ j. The crown graph can be viewed as a complete bipartite graph from which the edges of a perfect matching have been
Crown_graph
Creating a new graph from an existing graph
rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will
Graph_rewriting
Graph with nodes connected linearly
symmetric group. Path (graph theory) Ladder graph Caterpillar tree Complete graph Null graph Path decomposition Cycle (graph theory) While it is most
Path_graph
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
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
Planar graph with 5 nodes and 6 edges
non-graceful simple graphs with five vertices. One of them is the butterfly graph. The two others are cycle graph C5 and the complete graph K5. A graph is bowtie-free
Butterfly_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
Branch of mathematical combinatorics
consider a complete graph of order n; that is, there are n vertices and each vertex is connected to every other vertex by an edge. A complete graph of order
Ramsey_theory
COMPLETE GRAPH
COMPLETE GRAPH
Girl/Female
Indian
Complete
Boy/Male
Tamil
Complete
Boy/Male
Muslim
Complete
Boy/Male
Indian
Complete
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Girl/Female
Tamil
Complete
Boy/Male
Muslim
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Girl/Female
Indian
Complete
Girl/Female
Tamil
Complete
Boy/Male
Indian
Complete
Girl/Female
Muslim
Complete
Boy/Male
Muslim
Complete
Girl/Female
Australian, French, Greek
Victory of the People
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Complete
Girl/Female
Hindu
Complete
COMPLETE GRAPH
COMPLETE GRAPH
Boy/Male
Swedish
Noble or ready.
Girl/Female
Indian
Angel
Boy/Male
Australian, Italian, Portuguese
Has Many Skills
Boy/Male
Hindu, Indian, Punjabi, Sikh
True Servant
Girl/Female
Arabic, Muslim
Variety
Girl/Female
Hindu
Name of a Nakshathra, Months name
Girl/Female
Hindu, Indian
Praise of God
Female
Danish
, holy.
Female
Egyptian
, a goddess worshipped at Ten.
Boy/Male
Indian
Divine; Love
COMPLETE GRAPH
COMPLETE GRAPH
COMPLETE GRAPH
COMPLETE GRAPH
COMPLETE GRAPH
a.
Filled up; with no part or element lacking; free from deficiency; entire; perfect; consummate.
p. pr. & vb. n.
of Complete
a.
Perfect; complete.
a.
Complex, complicated.
a.
Having all the parts or organs which belong to it or to the typical form; having calyx, corolla, stamens, and pistil.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
A preparation of fruit in sirup in such a manner as to preserve its form, either whole, halved, or quartered; as, a compote of pears.
a.
Incomplete.
imp. & p. p.
of Compete
a.
Making complete.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
v. i.
To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.
a.
Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective.
n.
Complete annulment.
adv.
In a complete manner; fully.
imp. & p. p.
of Complete
adv.
In a whole or complete manner; entirely; completely; perfectly.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Full; complete.
n.
Complete termination.